diff --git a/common/djangoapps/student/models.py b/common/djangoapps/student/models.py
index 256751eb6d..fc3460628f 100644
--- a/common/djangoapps/student/models.py
+++ b/common/djangoapps/student/models.py
@@ -36,13 +36,15 @@ from importlib import import_module
 
 from opaque_keys.edx.locations import SlashSeparatedCourseKey
 
-from course_modes.models import CourseMode
 import lms.lib.comment_client as cc
 from util.query import use_read_replica_if_available
 from xmodule_django.models import CourseKeyField, NoneToEmptyManager
 from opaque_keys.edx.keys import CourseKey
 from functools import total_ordering
 
+from certificates.models import GeneratedCertificate
+from course_modes.models import CourseMode
+
 unenroll_done = Signal(providing_args=["course_enrollment"])
 log = logging.getLogger(__name__)
 AUDIT_LOG = logging.getLogger("audit")
@@ -953,6 +955,11 @@ class CourseEnrollment(models.Model):
         # (side-effects are bad)
         if getattr(self, 'can_refund', None) is not None:
             return True
+
+        # If the student has already been given a certificate they should not be refunded
+        if GeneratedCertificate.certificate_for_student(self.user, self.course_id) is not None:
+            return False
+
         course_mode = CourseMode.mode_for_course(self.course_id, 'verified')
         if course_mode is None:
             return False
diff --git a/common/djangoapps/student/tests/tests.py b/common/djangoapps/student/tests/tests.py
index c5845ac8bc..c241585021 100644
--- a/common/djangoapps/student/tests/tests.py
+++ b/common/djangoapps/student/tests/tests.py
@@ -30,6 +30,8 @@ from student.views import (process_survey_link, _cert_info,
                            change_enrollment, complete_course_mode_info)
 from student.tests.factories import UserFactory, CourseModeFactory
 
+from certificates.models import CertificateStatuses
+from certificates.tests.factories import GeneratedCertificateFactory
 import shoppingcart
 
 log = logging.getLogger(__name__)
@@ -216,6 +218,7 @@ class DashboardTest(TestCase):
         self.assertFalse(course_mode_info['show_upsell'])
         self.assertIsNone(course_mode_info['days_for_upsell'])
 
+    @unittest.skipUnless(settings.ROOT_URLCONF == 'lms.urls', 'Test only valid in lms')
     def test_refundable(self):
         verified_mode = CourseModeFactory.create(
             course_id=self.course.id,
@@ -231,6 +234,26 @@ class DashboardTest(TestCase):
         verified_mode.save()
         self.assertFalse(enrollment.refundable())
 
+    @unittest.skipUnless(settings.ROOT_URLCONF == 'lms.urls', 'Test only valid in lms')
+    def test_refundable_when_certificate_exists(self):
+        verified_mode = CourseModeFactory.create(
+            course_id=self.course.id,
+            mode_slug='verified',
+            mode_display_name='Verified',
+            expiration_datetime=datetime.now(pytz.UTC) + timedelta(days=1)
+        )
+        enrollment = CourseEnrollment.enroll(self.user, self.course.id, mode='verified')
+
+        self.assertTrue(enrollment.refundable())
+
+        generated_certificate = GeneratedCertificateFactory.create(
+            user=self.user,
+            course_id=self.course.id,
+            status=CertificateStatuses.downloadable,
+            mode='verified'
+        )
+
+        self.assertFalse(enrollment.refundable())
 
 
 class EnrollInCourseTest(TestCase):
diff --git a/lms/djangoapps/certificates/models.py b/lms/djangoapps/certificates/models.py
index 71ab9ffcf4..59af2f8ba9 100644
--- a/lms/djangoapps/certificates/models.py
+++ b/lms/djangoapps/certificates/models.py
@@ -80,6 +80,8 @@ class CertificateWhitelist(models.Model):
     whitelist = models.BooleanField(default=0)
 
 
+MODES = Choices('verified', 'honor', 'audit')
+
 class GeneratedCertificate(models.Model):
     user = models.ForeignKey(User)
     course_id = CourseKeyField(max_length=255, blank=True, default=None)
@@ -90,7 +92,6 @@ class GeneratedCertificate(models.Model):
     key = models.CharField(max_length=32, blank=True, default='')
     distinction = models.BooleanField(default=False)
     status = models.CharField(max_length=32, default='unavailable')
-    MODES = Choices('verified', 'honor', 'audit')
     mode = models.CharField(max_length=32, choices=MODES, default=MODES.honor)
     name = models.CharField(blank=True, max_length=255)
     created_date = models.DateTimeField(
@@ -102,6 +103,18 @@ class GeneratedCertificate(models.Model):
     class Meta:
         unique_together = (('user', 'course_id'),)
 
+    @classmethod
+    def certificate_for_student(cls, student, course_id):
+        """
+        This returns the certificate for a student for a particular course
+        or None if no such certificate exits.
+        """
+        try:
+            return cls.objects.get(user=student, course_id=course_id)
+        except cls.DoesNotExist:
+            pass
+
+        return None
 
 def certificate_status_for_student(student, course_id):
     '''
diff --git a/lms/djangoapps/certificates/tests/__init__.py b/lms/djangoapps/certificates/tests/__init__.py
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/lms/djangoapps/certificates/tests/factories.py b/lms/djangoapps/certificates/tests/factories.py
new file mode 100644
index 0000000000..e1d824b22a
--- /dev/null
+++ b/lms/djangoapps/certificates/tests/factories.py
@@ -0,0 +1,16 @@
+from factory.django import DjangoModelFactory
+
+from opaque_keys.edx.locations import SlashSeparatedCourseKey
+
+from certificates.models import GeneratedCertificate, CertificateStatuses, MODES
+
+# Factories don't have __init__ methods, and are self documenting
+# pylint: disable=W0232
+class GeneratedCertificateFactory(DjangoModelFactory):
+
+    FACTORY_FOR = GeneratedCertificate
+
+    course_id = None
+    status = CertificateStatuses.unavailable
+    mode = MODES.honor
+    name = ''