diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index abf574ae109fd7..406ca9ba045c96 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -205,6 +205,13 @@ Strings
 -
 -
 
+Interval
+^^^^^^^^
+
+- Bug in the :class:`IntervalIndex` constructor where the ``closed`` parameter did not always override the inferred ``closed`` (:issue:`19370`)
+-
+-
+
 Indexing
 ^^^^^^^^
 
diff --git a/pandas/_libs/interval.pyx b/pandas/_libs/interval.pyx
index 5dbf509fda65e6..fbb7265a17f8b6 100644
--- a/pandas/_libs/interval.pyx
+++ b/pandas/_libs/interval.pyx
@@ -335,11 +335,17 @@ cdef class Interval(IntervalMixin):
 
 @cython.wraparound(False)
 @cython.boundscheck(False)
-cpdef intervals_to_interval_bounds(ndarray intervals):
+cpdef intervals_to_interval_bounds(ndarray intervals,
+                                   bint validate_closed=True):
     """
     Parameters
     ----------
-    intervals: ndarray object array of Intervals / nulls
+    intervals : ndarray
+        object array of Intervals / nulls
+
+    validate_closed: boolean, default True
+        boolean indicating if all intervals must be closed on the same side.
+        Mismatching closed will raise if True, else return None for closed.
 
     Returns
     -------
@@ -353,6 +359,7 @@ cpdef intervals_to_interval_bounds(ndarray intervals):
         object closed = None, interval
         int64_t n = len(intervals)
         ndarray left, right
+        bint seen_closed = False
 
     left = np.empty(n, dtype=intervals.dtype)
     right = np.empty(n, dtype=intervals.dtype)
@@ -370,10 +377,14 @@ cpdef intervals_to_interval_bounds(ndarray intervals):
 
         left[i] = interval.left
         right[i] = interval.right
-        if closed is None:
+        if not seen_closed:
+            seen_closed = True
             closed = interval.closed
         elif closed != interval.closed:
-            raise ValueError('intervals must all be closed on the same side')
+            closed = None
+            if validate_closed:
+                msg = 'intervals must all be closed on the same side'
+                raise ValueError(msg)
 
     return left, right, closed
 
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index 23a655b9a51ee8..80619c7beb28c1 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -233,7 +233,7 @@ def __new__(cls, data, closed=None, dtype=None, copy=False,
         if isinstance(data, IntervalIndex):
             left = data.left
             right = data.right
-            closed = data.closed
+            closed = closed or data.closed
         else:
 
             # don't allow scalars
@@ -241,16 +241,8 @@ def __new__(cls, data, closed=None, dtype=None, copy=False,
                 cls._scalar_data_error(data)
 
             data = maybe_convert_platform_interval(data)
-            left, right, infer_closed = intervals_to_interval_bounds(data)
-
-            if (com._all_not_none(closed, infer_closed) and
-                    closed != infer_closed):
-                # GH 18421
-                msg = ("conflicting values for closed: constructor got "
-                       "'{closed}', inferred from data '{infer_closed}'"
-                       .format(closed=closed, infer_closed=infer_closed))
-                raise ValueError(msg)
-
+            left, right, infer_closed = intervals_to_interval_bounds(
+                data, validate_closed=closed is None)
             closed = closed or infer_closed
 
         return cls._simple_new(left, right, closed, name, copy=copy,
diff --git a/pandas/tests/indexes/interval/test_construction.py b/pandas/tests/indexes/interval/test_construction.py
index ac946a3421e539..3745f79d7d65d0 100644
--- a/pandas/tests/indexes/interval/test_construction.py
+++ b/pandas/tests/indexes/interval/test_construction.py
@@ -312,13 +312,7 @@ def test_generic_errors(self, constructor):
         pass
 
     def test_constructor_errors(self, constructor):
-        # mismatched closed inferred from intervals vs constructor.
-        ivs = [Interval(0, 1, closed='both'), Interval(1, 2, closed='both')]
-        msg = 'conflicting values for closed'
-        with tm.assert_raises_regex(ValueError, msg):
-            constructor(ivs, closed='neither')
-
-        # mismatched closed within intervals
+        # mismatched closed within intervals with no constructor override
         ivs = [Interval(0, 1, closed='right'), Interval(2, 3, closed='left')]
         msg = 'intervals must all be closed on the same side'
         with tm.assert_raises_regex(ValueError, msg):
@@ -336,6 +330,24 @@ def test_constructor_errors(self, constructor):
         with tm.assert_raises_regex(TypeError, msg):
             constructor([0, 1])
 
+    @pytest.mark.parametrize('data, closed', [
+        ([], 'both'),
+        ([np.nan, np.nan], 'neither'),
+        ([Interval(0, 3, closed='neither'),
+          Interval(2, 5, closed='neither')], 'left'),
+        ([Interval(0, 3, closed='left'),
+          Interval(2, 5, closed='right')], 'neither'),
+        (IntervalIndex.from_breaks(range(5), closed='both'), 'right')])
+    def test_override_inferred_closed(self, constructor, data, closed):
+        # GH 19370
+        if isinstance(data, IntervalIndex):
+            tuples = data.to_tuples()
+        else:
+            tuples = [(iv.left, iv.right) if notna(iv) else iv for iv in data]
+        expected = IntervalIndex.from_tuples(tuples, closed=closed)
+        result = constructor(data, closed=closed)
+        tm.assert_index_equal(result, expected)
+
 
 class TestFromIntervals(TestClassConstructors):
     """