diff --git a/qiskit_experiments/framework/experiment_data.py b/qiskit_experiments/framework/experiment_data.py
index 3428875086..6edbad6650 100644
--- a/qiskit_experiments/framework/experiment_data.py
+++ b/qiskit_experiments/framework/experiment_data.py
@@ -379,8 +379,10 @@ def completion_times(self) -> Dict[str, datetime]:
         """Returns the completion times of the jobs."""
         job_times = {}
         for job_id, job in self._jobs.items():
-            if job is not None and "COMPLETED" in job.time_per_step():
-                job_times[job_id] = job.time_per_step().get("COMPLETED")
+            if job is not None:
+                job_times[job_id] = job.time_per_step().get(
+                    "COMPLETED", None
+                ) or job.time_per_step().get("finished", None)
 
         return job_times
 
diff --git a/releasenotes/notes/completion_times_fix-6f8d5449d0de4a9d.yaml b/releasenotes/notes/completion_times_fix-6f8d5449d0de4a9d.yaml
new file mode 100644
index 0000000000..1e59d38de3
--- /dev/null
+++ b/releasenotes/notes/completion_times_fix-6f8d5449d0de4a9d.yaml
@@ -0,0 +1,5 @@
+---
+fixes:
+  - |
+    The :meth:`ExperimentData.completion_times` property was fixed to correctly
+    read the data from the `IBMCircuitJob` object.