diff --git a/qiskit/algorithms/optimizers/qnspsa.py b/qiskit/algorithms/optimizers/qnspsa.py
index 39e60090a8..b7ba297962 100644
--- a/qiskit/algorithms/optimizers/qnspsa.py
+++ b/qiskit/algorithms/optimizers/qnspsa.py
@@ -311,8 +311,18 @@ class QNSPSA(SPSA):
 
         fid = ComputeUncompute(sampler)
 
+        num_parameters = circuit.num_parameters
+
         def fidelity(values_x, values_y):
-            result = fid.run(circuit, circuit, values_x, values_y).result()
+            values_x = np.reshape(values_x, (-1, num_parameters)).tolist()
+            batch_size_x = len(values_x)
+
+            values_y = np.reshape(values_y, (-1, num_parameters)).tolist()
+            batch_size_y = len(values_y)
+
+            result = fid.run(
+                batch_size_x * [circuit], batch_size_y * [circuit], values_x, values_y
+            ).result()
             return np.asarray(result.fidelities)
 
         return fidelity
diff --git a/releasenotes/notes/fix-qnspsa-max-evals-grouped-52eb462fa6c82079.yaml b/releasenotes/notes/fix-qnspsa-max-evals-grouped-52eb462fa6c82079.yaml
new file mode 100644
index 0000000000..3b8209946f
--- /dev/null
+++ b/releasenotes/notes/fix-qnspsa-max-evals-grouped-52eb462fa6c82079.yaml
@@ -0,0 +1,5 @@
+---
+fixes:
+  - |
+    Fixes a bug causing QNSPSA to fail when ``max_evals_grouped`` was set to a
+    value larger than 1.
diff --git a/test/python/algorithms/optimizers/test_spsa.py b/test/python/algorithms/optimizers/test_spsa.py
index ad1c605a66..c18d498291 100644
--- a/test/python/algorithms/optimizers/test_spsa.py
+++ b/test/python/algorithms/optimizers/test_spsa.py
@@ -19,7 +19,7 @@ import numpy as np
 
 from qiskit.algorithms.optimizers import SPSA, QNSPSA
 from qiskit.circuit.library import PauliTwoDesign
-from qiskit.primitives import Sampler
+from qiskit.primitives import Estimator, Sampler
 from qiskit.providers.basicaer import StatevectorSimulatorPy
 from qiskit.opflow import I, Z, StateFn, MatrixExpectation
 from qiskit.utils import algorithm_globals
@@ -222,3 +222,36 @@ class TestSPSA(QiskitAlgorithmsTestCase):
             result = fidelity(initial_point, initial_point)
 
             self.assertAlmostEqual(result[0], 1)
+
+    def test_qnspsa_max_evals_grouped(self):
+        """Test using max_evals_grouped with QNSPSA."""
+        circuit = PauliTwoDesign(3, reps=1, seed=1)
+        num_parameters = circuit.num_parameters
+        obs = Z ^ Z ^ I
+
+        estimator = Estimator(options={"seed": 12})
+
+        initial_point = np.array(
+            [0.82311034, 0.02611798, 0.21077064, 0.61842177, 0.09828447, 0.62013131]
+        )
+
+        def objective(x):
+            x = np.reshape(x, (-1, num_parameters)).tolist()
+            n = len(x)
+            return estimator.run(n * [circuit], n * [obs.primitive], x).result().values.real
+
+        fidelity = QNSPSA.get_fidelity(circuit)
+        optimizer = QNSPSA(fidelity)
+        optimizer.maxiter = 1
+        optimizer.learning_rate = 0.05
+        optimizer.perturbation = 0.05
+        optimizer.set_max_evals_grouped(50)  # greater than 1
+
+        result = optimizer.minimize(objective, initial_point)
+
+        with self.subTest("check final accuracy"):
+            self.assertAlmostEqual(result.fun[0], 0.473, places=3)
+
+        with self.subTest("check number of function calls"):
+            expected_nfev = 8  # 7 * maxiter + 1
+            self.assertEqual(result.nfev, expected_nfev)