diff --git a/doc/whats_new/v1.0.rst b/doc/whats_new/v1.0.rst
index 40076c0b275dd..30c184db592a0 100644
--- a/doc/whats_new/v1.0.rst
+++ b/doc/whats_new/v1.0.rst
@@ -67,6 +67,15 @@ Fixed models
   names out from one step of a pipeline to the next. :pr:`21351` by
   `Thomas Fan`_.
 
+:mod:`sklearn.svm`
+..................
+
+- |Fix| :class:`svm.SVC` and :class:`svm.SVR` check for an inconsistency
+  in its internal representation and raise an error instead of segfaulting.
+  This fix also resolves
+  `CVE-2020-28975 <https://nvd.nist.gov/vuln/detail/CVE-2020-28975>`__.
+  :pr:`21336` by `Thomas Fan`_.
+
 .. _changes_1_0:
 
 Version 1.0.0
diff --git a/sklearn/svm/_base.py b/sklearn/svm/_base.py
index 9c992e0d1f1fa..7f0e628aab70c 100644
--- a/sklearn/svm/_base.py
+++ b/sklearn/svm/_base.py
@@ -616,6 +616,13 @@ def _validate_for_predict(self, X):
                     "the number of samples at training time"
                     % (X.shape[1], self.shape_fit_[0])
                 )
+        # Fixes https://nvd.nist.gov/vuln/detail/CVE-2020-28975
+        # Check that _n_support is consistent with support_vectors
+        sv = self.support_vectors_
+        if not self._sparse and sv.size > 0 and self.n_support_.sum() != sv.shape[0]:
+            raise ValueError(
+                f"The internal representation of {self.__class__.__name__} was altered"
+            )
         return X
 
     @property
diff --git a/sklearn/svm/tests/test_svm.py b/sklearn/svm/tests/test_svm.py
index 3933b6ca029e2..eb15aca0096b8 100644
--- a/sklearn/svm/tests/test_svm.py
+++ b/sklearn/svm/tests/test_svm.py
@@ -1371,3 +1371,16 @@ def string_kernel(X1, X2):
     else:  # regressor
         assert_allclose(svc1.predict(data), svc2.predict(X))
         assert_allclose(svc1.predict(data), svc3.predict(K))
+
+
+def test_svc_raises_error_internal_representation():
+    """Check that SVC raises error when internal representation is altered.
+
+    Non-regression test for #18891 and https://nvd.nist.gov/vuln/detail/CVE-2020-28975
+    """
+    clf = svm.SVC(kernel="linear").fit(X, Y)
+    clf._n_support[0] = 1000000
+
+    msg = "The internal representation of SVC was altered"
+    with pytest.raises(ValueError, match=msg):
+        clf.predict(X)