diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 6cf2720a033..48323ee629c 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -25,10 +25,11 @@ Enhancements
 Bug fixes
 ~~~~~~~~~
 
+- Dataset.copy(deep=True) now creates a deep copy of the attrs (:issue:`2835`).
+  By `Andras Gefferth <https://github.com/kefirbandi>`_.
 - ``swap_dims`` would create incorrect ``indexes`` (:issue:`2842`).
   By `Stephan Hoyer <https://github.com/shoyer>`_.
 
-
 .. _whats-new.0.12.0:
 
 v0.12.0 (15 March 2019)
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 3bb54e80456..4ee70002102 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -915,7 +915,9 @@ def copy(self: T, deep: bool = False, data: Mapping = None) -> T:
             variables = OrderedDict((k, v.copy(deep=deep, data=data.get(k)))
                                     for k, v in self._variables.items())
 
-        return self._replace(variables)
+        attrs = copy.deepcopy(self._attrs) if deep else copy.copy(self._attrs)
+
+        return self._replace(variables, attrs=attrs)
 
     @property
     def _level_coords(self):
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index 777a8e84a3f..ad59cede5f4 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -1885,6 +1885,7 @@ def test_drop_dims(self):
 
     def test_copy(self):
         data = create_test_data()
+        data.attrs['Test'] = [1, 2, 3]
 
         for copied in [data.copy(deep=False), copy(data)]:
             assert_identical(data, copied)
@@ -1899,12 +1900,18 @@ def test_copy(self):
             copied['foo'] = ('z', np.arange(5))
             assert 'foo' not in data
 
+            copied.attrs['foo'] = 'bar'
+            assert 'foo' not in data.attrs
+            assert data.attrs['Test'] is copied.attrs['Test']
+
         for copied in [data.copy(deep=True), deepcopy(data)]:
             assert_identical(data, copied)
             for k, v0 in data.variables.items():
                 v1 = copied.variables[k]
                 assert v0 is not v1
 
+            assert data.attrs['Test'] is not copied.attrs['Test']
+
     def test_copy_with_data(self):
         orig = create_test_data()
         new_data = {k: np.random.randn(*v.shape)