diff --git a/qiskit/aqua/algorithms/minimum_eigen_solvers/qaoa/qaoa.py b/qiskit/aqua/algorithms/minimum_eigen_solvers/qaoa/qaoa.py
index 46888ca477..245c7538d6 100755
--- a/qiskit/aqua/algorithms/minimum_eigen_solvers/qaoa/qaoa.py
+++ b/qiskit/aqua/algorithms/minimum_eigen_solvers/qaoa/qaoa.py
@@ -123,6 +123,8 @@ def __init__(self,
     @VQE.operator.setter
     def operator(self, operator: Union[OperatorBase, LegacyBaseOperator]) -> None:
         """ Sets operator """
+        # Need to wipe the var_form in case number of qubits differs from operator.
+        self.var_form = None
         # Setting with VQE's operator property
         super(QAOA, self.__class__).operator.__set__(self, operator)
         self.var_form = QAOAVarForm(self.operator,
diff --git a/qiskit/aqua/algorithms/minimum_eigen_solvers/vqe.py b/qiskit/aqua/algorithms/minimum_eigen_solvers/vqe.py
index f9656aa340..46a9a0a404 100755
--- a/qiskit/aqua/algorithms/minimum_eigen_solvers/vqe.py
+++ b/qiskit/aqua/algorithms/minimum_eigen_solvers/vqe.py
@@ -131,7 +131,9 @@ def __init__(self,
 
         self._max_evals_grouped = max_evals_grouped
         self._circuit_sampler = None
+        self._expectation = expectation
         self._expect_op = None
+        self._operator = None
 
         super().__init__(var_form=var_form,
                          optimizer=optimizer,
@@ -143,8 +145,6 @@ def __init__(self,
         self._optimizer.set_max_evals_grouped(max_evals_grouped)
         self._callback = callback
 
-        self._expectation = expectation
-        self._operator = None
         if operator is not None:
             self.operator = operator
         self.aux_operators = aux_operators
diff --git a/qiskit/aqua/algorithms/vq_algorithm.py b/qiskit/aqua/algorithms/vq_algorithm.py
index b394f31d79..f74938a163 100644
--- a/qiskit/aqua/algorithms/vq_algorithm.py
+++ b/qiskit/aqua/algorithms/vq_algorithm.py
@@ -84,7 +84,7 @@ def var_form(self) -> Optional[Union[QuantumCircuit, VariationalForm]]:
         return self._var_form
 
     @var_form.setter
-    def var_form(self, var_form: Union[QuantumCircuit, VariationalForm]):
+    def var_form(self, var_form: Optional[Union[QuantumCircuit, VariationalForm]]):
         """ Sets variational form """
         if isinstance(var_form, QuantumCircuit):
             # store the parameters
@@ -93,6 +93,9 @@ def var_form(self, var_form: Union[QuantumCircuit, VariationalForm]):
         elif isinstance(var_form, VariationalForm):
             self._var_form_params = ParameterVector('θ', length=var_form.num_parameters)
             self._var_form = var_form
+        elif var_form is None:
+            self._var_form_params = None
+            self._var_form = var_form
         else:
             raise ValueError(
                 "Unsupported type '{}' of var_form".format(
diff --git a/test/optimization/test_qaoa.py b/test/optimization/test_qaoa.py
index 72734889e4..f97242fdef 100755
--- a/test/optimization/test_qaoa.py
+++ b/test/optimization/test_qaoa.py
@@ -26,7 +26,7 @@
 from qiskit.aqua.components.optimizers import COBYLA
 from qiskit.aqua.algorithms import QAOA
 from qiskit.aqua import QuantumInstance, aqua_globals
-from qiskit.aqua.operators import WeightedPauliOperator
+from qiskit.aqua.operators import WeightedPauliOperator, X, Z
 
 W1 = np.array([
     [0, 1, 0, 1],
@@ -90,6 +90,21 @@ def test_qaoa(self, w, prob, m, solutions, convert_to_matrix_op):
         self.log.debug('solution objective: %s', max_cut.max_cut_value(x, w))
         self.assertIn(''.join([str(int(i)) for i in graph_solution]), solutions)
 
+    def test_change_operator_size(self):
+        """ QAOA test """
+        backend = BasicAer.get_backend('statevector_simulator')
+        optimizer = COBYLA(maxiter=2)
+        qubit_op, _ = max_cut.get_operator(W1)
+        qubit_op = qubit_op.to_opflow().to_matrix_op()
+
+        seed = 0
+        aqua_globals.random_seed = seed
+        qaoa = QAOA(qubit_op, optimizer, P1)
+        quantum_instance = QuantumInstance(backend, seed_simulator=seed, seed_transpiler=seed)
+        qaoa.run(quantum_instance)
+        qaoa.operator = (X ^ qubit_op ^ Z)
+        qaoa.run()
+
 
 if __name__ == '__main__':
     unittest.main()