googleapis
diff --git a/google/cloud/bigquery/dbapi/types.py b/google/cloud/bigquery/dbapi/types.py
@@ -30,16 +30,28 @@
 TimestampFromTicks = datetime.datetime.fromtimestamp
 
 
-def Binary(string):
+def Binary(data):
     """Contruct a DB-API binary value.
 
     Args:
-        string (str): A string to encode as a binary value.
+        data (bytes-like): An object containing binary data and that
+                           can be converted to bytes with the `bytes` builtin.
 
     Returns:
-        bytes: The UTF-8 encoded bytes representing the string.
+        bytes: The binary data as a bytes object.
     """
-    return string.encode("utf-8")
+    if isinstance(data, int):
+        # This is not the conversion we're looking for, because it
+        # will simply create a bytes object of the given size.
+        raise TypeError("cannot convert `int` object to binary")
+
+    try:
+        return bytes(data)
+    except TypeError:
+        if isinstance(data, str):
+            return data.encode("utf-8")
+        else:
+            raise
 
 
 def TimeFromTicks(ticks, tz=None):

diff --git a/tests/unit/test_dbapi_types.py b/tests/unit/test_dbapi_types.py
@@ -15,6 +15,8 @@
 import datetime
 import unittest
 
+import pytest
+
 import google.cloud._helpers
 from google.cloud.bigquery.dbapi import types
 
@@ -26,10 +28,6 @@ def test_binary_type(self):
         self.assertEqual("STRUCT", types.BINARY)
         self.assertNotEqual("STRING", types.BINARY)
 
-    def test_binary_constructor(self):
-        self.assertEqual(types.Binary(u"hello"), b"hello")
-        self.assertEqual(types.Binary(u"\u1f60"), u"\u1f60".encode("utf-8"))
-
     def test_timefromticks(self):
         somedatetime = datetime.datetime(
             2017, 2, 18, 12, 47, 26, tzinfo=google.cloud._helpers.UTC
@@ -40,3 +38,29 @@ def test_timefromticks(self):
             types.TimeFromTicks(ticks, google.cloud._helpers.UTC),
             datetime.time(12, 47, 26, tzinfo=google.cloud._helpers.UTC),
         )
+
+
+class CustomBinary:
+    def __bytes__(self):
+        return b"Google"
+
+
+@pytest.mark.parametrize(
+    "raw,expected",
+    [
+        (u"hello", b"hello"),
+        (u"\u1f60", u"\u1f60".encode("utf-8")),
+        (b"hello", b"hello"),
+        (bytearray(b"hello"), b"hello"),
+        (memoryview(b"hello"), b"hello"),
+        (CustomBinary(), b"Google"),
+    ],
+)
+def test_binary_constructor(raw, expected):
+    assert types.Binary(raw) == expected
+
+
+@pytest.mark.parametrize("bad", (42, 42.0, None))
+def test_invalid_binary_constructor(bad):
+    with pytest.raises(TypeError):
+        types.Binary(bad)