diff --git a/qiskit/circuit/library/blueprintcircuit.py b/qiskit/circuit/library/blueprintcircuit.py
index 958b1b65c2db..7d339f11ae3e 100644
--- a/qiskit/circuit/library/blueprintcircuit.py
+++ b/qiskit/circuit/library/blueprintcircuit.py
@@ -100,6 +100,16 @@ def append(self, instruction, qargs=None, cargs=None):
             self._build()
         return super().append(instruction, qargs, cargs)
 
+    def compose(self, other, qubits=None, clbits=None, front=False, inplace=False):
+        if self._data is None:
+            self._build()
+        return super().compose(other, qubits, clbits, front, inplace)
+
+    def inverse(self):
+        if self._data is None:
+            self._build()
+        return super().inverse()
+
     def __len__(self):
         return len(self.data)
 
diff --git a/releasenotes/notes/build-blueprintcircuit-before-inverse-8ef85f6389588fe0.yaml b/releasenotes/notes/build-blueprintcircuit-before-inverse-8ef85f6389588fe0.yaml
new file mode 100644
index 000000000000..a8be8850b7b3
--- /dev/null
+++ b/releasenotes/notes/build-blueprintcircuit-before-inverse-8ef85f6389588fe0.yaml
@@ -0,0 +1,6 @@
+---
+fixes:
+  - |
+    Calling inverse or compose on a ``BlueprintCircuit`` could fail
+    if ``_data`` was not yet populated. This has been fixed by asserting
+    a call on ``_build`` method.
diff --git a/test/python/circuit/library/test_blueprintcircuit.py b/test/python/circuit/library/test_blueprintcircuit.py
index 36e42f640285..701085541e00 100644
--- a/test/python/circuit/library/test_blueprintcircuit.py
+++ b/test/python/circuit/library/test_blueprintcircuit.py
@@ -15,7 +15,7 @@
 import unittest
 
 from qiskit.test.base import QiskitTestCase
-from qiskit.circuit import QuantumRegister, Parameter
+from qiskit.circuit import QuantumRegister, Parameter, QuantumCircuit
 from qiskit.circuit.library import BlueprintCircuit
 
 
@@ -90,7 +90,7 @@ def test_calling_attributes_works(self):
                 self.assertGreater(len(circuit._data), 0)
 
         methods = ['qasm', 'count_ops', 'num_connected_components', 'num_nonlocal_gates',
-                   'depth', '__len__', 'copy']
+                   'depth', '__len__', 'copy', 'inverse']
         for method in methods:
             with self.subTest(method=method):
                 circuit = MockBlueprint(3)
@@ -102,6 +102,20 @@ def test_calling_attributes_works(self):
             _ = circuit[2]
             self.assertGreater(len(circuit._data), 0)
 
+    def test_compose_works(self):
+        """Test that the circuit is constructed when compose is called."""
+        qc = QuantumCircuit(3)
+        qc.x([0, 1, 2])
+        circuit = MockBlueprint(3)
+        circuit.compose(qc, inplace=True)
+
+        reference = QuantumCircuit(3)
+        reference.rx(list(circuit.parameters)[0], 0)
+        reference.h([0, 1, 2])
+        reference.x([0, 1, 2])
+
+        self.assertEqual(reference, circuit)
+
 
 if __name__ == '__main__':
     unittest.main()