diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index e5488b7a26..5b79723976 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -160,3 +160,67 @@ jobs:
       - uses: actions/upload-artifact@v2
         with:
           path: ./wheelhouse/*.whl
+  wheel-gpu-cu11:
+    runs-on: "ubuntu-latest"
+    steps:
+      - name: Maximize build space
+        uses: easimon/maximize-build-space@master
+        with:
+          root-reserve-mb: 30000
+          swap-size-mb: 1024
+          remove-dotnet: 'true'
+          remove-android: 'true'
+          remove-haskell: 'true'
+          remove-codeql: 'true'
+      - uses: actions/checkout@v3
+      - uses: actions/setup-python@v4
+        name: Install Python
+        with:
+          python-version: '3.8'
+      - name: Install cibuildwheel
+        run: |
+          python -m pip install cibuildwheel==2.16.2
+      - name: Build wheels
+        env:
+          CIBW_BEFORE_ALL: "yum install -y yum-utils wget && wget -q https://developer.download.nvidia.com/compute/cuda/11.8.0/local_installers/cuda-repo-rhel7-11-8-local-11.8.0_520.61.05-1.x86_64.rpm && rpm -i cuda-repo-rhel7-11-8-local-11.8.0_520.61.05-1.x86_64.rpm && yum clean all && yum -y install cuda && yum -y install openblas-devel && yum-config-manager --add-repo https://developer.download.nvidia.com/compute/cuda/repos/rhel7/x86_64/cuda-rhel7.repo && yum clean all"
+          CIBW_BEFORE_BUILD : "pip install nvidia-cuda-runtime-cu11 nvidia-cublas-cu11 nvidia-cusolver-cu11 nvidia-cusparse-cu11 cuquantum-cu11"
+          CIBW_SKIP: "*-manylinux_i686 pp* cp36* cp37* cp38* cp39* cp310* cp311* *musllinux*"
+          CIBW_ENVIRONMENT: QISKIT_AER_PACKAGE_NAME=qiskit-aer-gpu-cu11 QISKIT_AER_CUDA_MAJOR=11 CMAKE_VERBOSE_MAKEFILE=true AER_THRUST_BACKEND=CUDA CUDACXX=/usr/local/cuda/bin/nvcc AER_CUDA_ARCH="7.0 7.2 7.5 8.0 8.6 8.7" AER_PYTHON_CUDA_ROOT=/opt/_internal AER_CIBUILD=true
+          CIBW_REPAIR_WHEEL_COMMAND: 'auditwheel repair --exclude libcudart.so.11.0 --exclude libcustatevec.so.1 --exclude libcutensornet.so.2 --exclude libcutensor.so.1 --exclude libcutensorMg.so.1 --exclude libcusolver.so.11 --exclude libcusolverMg.so.11 --exclude libcusparse.so.11 --exclude libcublas.so.11 --exclude libcublasLt.so.11 -w {dest_dir} {wheel}'
+        run: |
+          python -m cibuildwheel --output-dir wheelhouse
+      - uses: actions/upload-artifact@v3
+        with:
+          path: ./wheelhouse/*.whl
+  wheel-gpu:
+    runs-on: "ubuntu-latest"
+    steps:
+      - name: Maximize build space
+        uses: easimon/maximize-build-space@master
+        with:
+          root-reserve-mb: 30000
+          swap-size-mb: 1024
+          remove-dotnet: 'true'
+          remove-android: 'true'
+          remove-haskell: 'true'
+          remove-codeql: 'true'
+      - uses: actions/checkout@v3
+      - uses: actions/setup-python@v4
+        name: Install Python
+        with:
+          python-version: '3.8'
+      - name: Install cibuildwheel
+        run: |
+          python -m pip install cibuildwheel==2.16.2
+      - name: Build wheels
+        env:
+          CIBW_BEFORE_ALL: "yum install -y yum-utils wget && wget -q https://developer.download.nvidia.com/compute/cuda/12.4.0/local_installers/cuda-repo-rhel7-12-4-local-12.4.0_550.54.14-1.x86_64.rpm && rpm -i cuda-repo-rhel7-12-4-local-12.4.0_550.54.14-1.x86_64.rpm && yum clean all && yum -y install nvidia-driver-latest-dkms && yum -y install cuda-toolkit-12-4 && yum -y install openblas-devel && yum clean all"
+          CIBW_BEFORE_BUILD : "pip install nvidia-cuda-runtime-cu12 nvidia-nvjitlink-cu12 nvidia-cublas-cu12 nvidia-cusolver-cu12 nvidia-cusparse-cu12 cuquantum-cu12"
+          CIBW_SKIP: "*-manylinux_i686 pp* cp36* cp37* cp38* cp39* cp310* cp311* *musllinux*"
+          CIBW_ENVIRONMENT: QISKIT_AER_PACKAGE_NAME=qiskit-aer-gpu QISKIT_AER_CUDA_MAJOR=12 CMAKE_VERBOSE_MAKEFILE=true AER_THRUST_BACKEND=CUDA CUDACXX=/usr/local/cuda/bin/nvcc AER_CUDA_ARCH="7.0 7.2 7.5 8.0 8.6 8.7 8.9 9.0" AER_PYTHON_CUDA_ROOT=/opt/_internal AER_CIBUILD=true
+          CIBW_REPAIR_WHEEL_COMMAND: 'auditwheel repair --exclude libcudart.so.12 --exclude libcustatevec.so.1 --exclude libcutensornet.so.2 --exclude libcutensor.so.1 --exclude libcutensorMg.so.1 --exclude libcusolver.so.11 --exclude libcusolverMg.so.11 --exclude libcusolver.so.12 --exclude libcusolverMg.so.12 --exclude libcusparse.so.12 --exclude libcublas.so.12 --exclude libcublasLt.so.12 --exclude libnvJitLink.so.12 -w {dest_dir} {wheel}'
+        run: |
+          python -m cibuildwheel --output-dir wheelhouse
+      - uses: actions/upload-artifact@v3
+        with:
+          path: ./wheelhouse/*.whl
diff --git a/.github/workflows/deploy.yml b/.github/workflows/deploy.yml
index a5a9d82cae..214046b752 100644
--- a/.github/workflows/deploy.yml
+++ b/.github/workflows/deploy.yml
@@ -130,7 +130,7 @@ jobs:
       - name: Maximize build space
         uses: easimon/maximize-build-space@master
         with:
-          root-reserve-mb: 40000
+          root-reserve-mb: 30000
           swap-size-mb: 1024
           remove-dotnet: 'true'
           remove-android: 'true'
@@ -173,7 +173,7 @@ jobs:
       - name: Maximize build space
         uses: easimon/maximize-build-space@master
         with:
-          root-reserve-mb: 40000
+          root-reserve-mb: 30000
           swap-size-mb: 1024
           remove-dotnet: 'true'
           remove-android: 'true'
@@ -189,7 +189,7 @@ jobs:
           python -m pip install cibuildwheel==2.16.2
       - name: Build wheels
         env:
-          CIBW_BEFORE_ALL: "yum install -y yum-utils wget && wget -q https://developer.download.nvidia.com/compute/cuda/12.2.2/local_installers/cuda-repo-rhel7-12-2-local-12.2.2_535.104.05-1.x86_64.rpm && rpm -i cuda-repo-rhel7-12-2-local-12.2.2_535.104.05-1.x86_64.rpm && yum clean all && yum -y install nvidia-driver-latest-dkms && yum -y install cuda && yum -y install openblas-devel && yum-config-manager --add-repo https://developer.download.nvidia.com/compute/cuda/repos/rhel7/x86_64/cuda-rhel7.repo && yum clean all"
+          CIBW_BEFORE_ALL: "yum install -y yum-utils wget && wget -q https://developer.download.nvidia.com/compute/cuda/12.4.0/local_installers/cuda-repo-rhel7-12-4-local-12.4.0_550.54.14-1.x86_64.rpm && rpm -i cuda-repo-rhel7-12-4-local-12.4.0_550.54.14-1.x86_64.rpm && yum clean all && yum -y install nvidia-driver-latest-dkms && yum -y install cuda-toolkit-12-4 && yum -y install openblas-devel && yum clean all"
           CIBW_BEFORE_BUILD : "pip install nvidia-cuda-runtime-cu12 nvidia-nvjitlink-cu12 nvidia-cublas-cu12 nvidia-cusolver-cu12 nvidia-cusparse-cu12 cuquantum-cu12"
           CIBW_SKIP: "*-manylinux_i686 pp* cp36* cp37* *musllinux*"
           CIBW_ENVIRONMENT: QISKIT_AER_PACKAGE_NAME=qiskit-aer-gpu QISKIT_AER_CUDA_MAJOR=12 CMAKE_VERBOSE_MAKEFILE=true AER_THRUST_BACKEND=CUDA CUDACXX=/usr/local/cuda/bin/nvcc AER_CUDA_ARCH="7.0 7.2 7.5 8.0 8.6 8.7 9.0" AER_PYTHON_CUDA_ROOT=/opt/_internal AER_CIBUILD=true
diff --git a/releasenotes/notes/add_gpu_build_test-2a95842b524c880b.yaml b/releasenotes/notes/add_gpu_build_test-2a95842b524c880b.yaml
new file mode 100644
index 0000000000..fa69b88819
--- /dev/null
+++ b/releasenotes/notes/add_gpu_build_test-2a95842b524c880b.yaml
@@ -0,0 +1,5 @@
+---
+features:
+  - |
+    Adding build test for qiskit-aer-cuda. Because GPU build takes long time,
+    it only tests building on Python 3.12 environment.