diff --git a/django/db/migrations/loader.py b/django/db/migrations/loader.py
index a5b7cce393..d459f2c524 100644
--- a/django/db/migrations/loader.py
+++ b/django/db/migrations/loader.py
@@ -280,6 +280,11 @@ class MigrationLoader(object):
                 continue
             for parent in self.graph.node_map[migration].parents:
                 if parent not in applied:
+                    # Skip unapplied squashed migrations that have all of their
+                    # `replaces` applied.
+                    if parent in self.replacements:
+                        if all(m in applied for m in self.replacements[parent].replaces):
+                            continue
                     raise InconsistentMigrationHistory(
                         "Migration {}.{} is applied before its dependency {}.{}".format(
                             migration[0], migration[1], parent[0], parent[1],
diff --git a/docs/releases/1.10.1.txt b/docs/releases/1.10.1.txt
index 8f0756bb9e..89fc2b2b19 100644
--- a/docs/releases/1.10.1.txt
+++ b/docs/releases/1.10.1.txt
@@ -29,3 +29,7 @@ Bugfixes
 
 * Fixed the ``isnull`` lookup on a ``ForeignKey`` with its ``to_field``
   pointing to a ``CharField`` (:ticket:`26983`).
+
+* Prevented the ``migrate`` command from raising
+  ``InconsistentMigrationHistory`` in the presence of unapplied squashed
+  migrations (:ticket:`27004`).
diff --git a/tests/migrations/test_loader.py b/tests/migrations/test_loader.py
index 0b014f7d57..c97cddb913 100644
--- a/tests/migrations/test_loader.py
+++ b/tests/migrations/test_loader.py
@@ -381,6 +381,23 @@ class LoaderTests(TestCase):
         with self.assertRaisesMessage(InconsistentMigrationHistory, msg):
             loader.check_consistent_history(connection)
 
+    @override_settings(
+        MIGRATION_MODULES={'migrations': 'migrations.test_migrations_squashed_extra'},
+        INSTALLED_APPS=['migrations'],
+    )
+    def test_check_consistent_history_squashed(self):
+        """
+        MigrationLoader.check_consistent_history() should ignore unapplied
+        squashed migrations that have all of their `replaces` applied.
+        """
+        loader = MigrationLoader(connection=None)
+        recorder = MigrationRecorder(connection)
+        recorder.record_applied('migrations', '0001_initial')
+        recorder.record_applied('migrations', '0002_second')
+        loader.check_consistent_history(connection)
+        recorder.record_applied('migrations', '0003_third')
+        loader.check_consistent_history(connection)
+
     @override_settings(MIGRATION_MODULES={
         "app1": "migrations.test_migrations_squashed_ref_squashed.app1",
         "app2": "migrations.test_migrations_squashed_ref_squashed.app2",
diff --git a/tests/migrations/test_migrations_squashed_extra/0001_initial.py b/tests/migrations/test_migrations_squashed_extra/0001_initial.py
new file mode 100644
index 0000000000..9a330e1067
--- /dev/null
+++ b/tests/migrations/test_migrations_squashed_extra/0001_initial.py
@@ -0,0 +1,8 @@
+# -*- coding: utf-8 -*-
+from __future__ import unicode_literals
+
+from django.db import migrations
+
+
+class Migration(migrations.Migration):
+    pass
diff --git a/tests/migrations/test_migrations_squashed_extra/0001_squashed_0002.py b/tests/migrations/test_migrations_squashed_extra/0001_squashed_0002.py
new file mode 100644
index 0000000000..79beebea1c
--- /dev/null
+++ b/tests/migrations/test_migrations_squashed_extra/0001_squashed_0002.py
@@ -0,0 +1,11 @@
+# -*- coding: utf-8 -*-
+from __future__ import unicode_literals
+
+from django.db import migrations
+
+
+class Migration(migrations.Migration):
+    replaces = [
+        ("migrations", "0001_initial"),
+        ("migrations", "0002_second"),
+    ]
diff --git a/tests/migrations/test_migrations_squashed_extra/0002_second.py b/tests/migrations/test_migrations_squashed_extra/0002_second.py
new file mode 100644
index 0000000000..4b892a7e8b
--- /dev/null
+++ b/tests/migrations/test_migrations_squashed_extra/0002_second.py
@@ -0,0 +1,8 @@
+# -*- coding: utf-8 -*-
+from __future__ import unicode_literals
+
+from django.db import migrations
+
+
+class Migration(migrations.Migration):
+    dependencies = [("migrations", "0001_initial")]
diff --git a/tests/migrations/test_migrations_squashed_extra/0003_third.py b/tests/migrations/test_migrations_squashed_extra/0003_third.py
new file mode 100644
index 0000000000..b69ae8883b
--- /dev/null
+++ b/tests/migrations/test_migrations_squashed_extra/0003_third.py
@@ -0,0 +1,8 @@
+# -*- coding: utf-8 -*-
+from __future__ import unicode_literals
+
+from django.db import migrations
+
+
+class Migration(migrations.Migration):
+    dependencies = [("migrations", "0002_second")]
diff --git a/tests/migrations/test_migrations_squashed_extra/__init__.py b/tests/migrations/test_migrations_squashed_extra/__init__.py
new file mode 100644
index 0000000000..e69de29bb2