diff --git a/sdk/storage/azblob/CHANGELOG.md b/sdk/storage/azblob/CHANGELOG.md
index 7270e1383744..24361be162e2 100644
--- a/sdk/storage/azblob/CHANGELOG.md
+++ b/sdk/storage/azblob/CHANGELOG.md
@@ -7,6 +7,7 @@
 ### Breaking Changes
 
 ### Bugs Fixed
+* Fix concurrency issue while Downloading File. Fixes [#22156](https://github.com/Azure/azure-sdk-for-go/issues/22156). 
 
 ### Other Changes
 
diff --git a/sdk/storage/azblob/blob/client.go b/sdk/storage/azblob/blob/client.go
index 5b3cf5544550..8f651a835f22 100644
--- a/sdk/storage/azblob/blob/client.go
+++ b/sdk/storage/azblob/blob/client.go
@@ -9,6 +9,7 @@ package blob
 import (
 	"context"
 	"io"
+	"math"
 	"os"
 	"sync"
 	"time"
@@ -469,23 +470,18 @@ func (b *Client) downloadFile(ctx context.Context, writer io.Writer, o downloadO
 
 	buffers := shared.NewMMBPool(int(o.Concurrency), o.BlockSize)
 	defer buffers.Free()
-	acquireBuffer := func() ([]byte, error) {
-		select {
-		case b := <-buffers.Acquire():
-			// got a buffer
-			return b, nil
-		default:
-			// no buffer available; allocate a new buffer if possible
-			if _, err := buffers.Grow(); err != nil {
-				return nil, err
-			}
 
-			// either grab the newly allocated buffer or wait for one to become available
-			return <-buffers.Acquire(), nil
+	numChunks := uint16((count-1)/o.BlockSize + 1)
+	for bufferCounter := float64(0); bufferCounter < math.Min(float64(numChunks), float64(o.Concurrency)); bufferCounter++ {
+		if _, err := buffers.Grow(); err != nil {
+			return 0, err
 		}
 	}
 
-	numChunks := uint16((count-1)/o.BlockSize) + 1
+	acquireBuffer := func() ([]byte, error) {
+		return <-buffers.Acquire(), nil
+	}
+
 	blocks := make([]chan []byte, numChunks)
 	for b := range blocks {
 		blocks[b] = make(chan []byte)