diff --git a/sqlite_utils/db.py b/sqlite_utils/db.py
index 80ad026..b8e8d4b 100644
--- a/sqlite_utils/db.py
+++ b/sqlite_utils/db.py
@@ -336,6 +336,10 @@ class Database:
         self._registered_functions: set = set()
         self.use_counts_table = use_counts_table
 
+    def close(self):
+        "Close the SQLite connection, and the underlying database file"
+        self.conn.close()
+
     @contextlib.contextmanager
     def tracer(self, tracer: Callable = None):
         """
diff --git a/tests/test_constructor.py b/tests/test_constructor.py
index d8c8d72..8743911 100644
--- a/tests/test_constructor.py
+++ b/tests/test_constructor.py
@@ -1,4 +1,6 @@
 from sqlite_utils import Database
+from sqlite_utils.utils import sqlite3
+import pytest
 
 
 def test_recursive_triggers():
@@ -25,3 +27,15 @@ def test_sqlite_version():
     as_string = ".".join(map(str, version))
     actual = next(db.query("select sqlite_version() as v"))["v"]
     assert actual == as_string
+
+
+@pytest.mark.parametrize("memory", [True, False])
+def test_database_close(tmpdir, memory):
+    if memory:
+        db = Database(memory=True)
+    else:
+        db = Database(str(tmpdir / "test.db"))
+    assert db.execute("select 1 + 1").fetchone()[0] == 2
+    db.close()
+    with pytest.raises(sqlite3.ProgrammingError):
+        db.execute("select 1 + 1")