diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index d2a4b32a71f..b913579d51f 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -84,6 +84,8 @@ Bug fixes
 - Fix :py:meth:`xarray.core.groupby.DataArrayGroupBy.reduce` and
   :py:meth:`xarray.core.groupby.DatasetGroupBy.reduce` when reducing over multiple dimensions.
   (:issue:`3402`). By `Deepak Cherian <https://github.com/dcherian/>`_
+- Allow appending datetime and bool data variables to zarr stores.
+  (:issue:`3480`). By `Akihiro Matsukawa <https://github.com/amatsukawa/>`_.
 
 Documentation
 ~~~~~~~~~~~~~
diff --git a/xarray/backends/api.py b/xarray/backends/api.py
index d23594fc675..945b3937c43 100644
--- a/xarray/backends/api.py
+++ b/xarray/backends/api.py
@@ -1234,6 +1234,8 @@ def _validate_datatypes_for_zarr_append(dataset):
     def check_dtype(var):
         if (
             not np.issubdtype(var.dtype, np.number)
+            and not np.issubdtype(var.dtype, np.datetime64)
+            and not np.issubdtype(var.dtype, np.bool)
             and not coding.strings.is_unicode_dtype(var.dtype)
             and not var.dtype == object
         ):
@@ -1241,8 +1243,9 @@ def check_dtype(var):
             raise ValueError(
                 "Invalid dtype for data variable: {} "
                 "dtype must be a subtype of number, "
-                "a fixed sized string, a fixed size "
-                "unicode string or an object".format(var)
+                "datetime, bool, a fixed sized string, "
+                "a fixed size unicode string or an "
+                "object".format(var)
             )
 
     for k in dataset.data_vars.values():
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index 50e78c9f685..39ef5a2bda1 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -90,6 +90,14 @@ def create_append_test_data(seed=None):
     string_var = np.array(["ae", "bc", "df"], dtype=object)
     string_var_to_append = np.array(["asdf", "asdfg"], dtype=object)
     unicode_var = ["áó", "áó", "áó"]
+    datetime_var = np.array(
+        ["2019-01-01", "2019-01-02", "2019-01-03"], dtype="datetime64[s]"
+    )
+    datetime_var_to_append = np.array(
+        ["2019-01-04", "2019-01-05"], dtype="datetime64[s]"
+    )
+    bool_var = np.array([True, False, True], dtype=np.bool)
+    bool_var_to_append = np.array([False, True], dtype=np.bool)
 
     ds = xr.Dataset(
         data_vars={
@@ -102,6 +110,8 @@ def create_append_test_data(seed=None):
             "unicode_var": xr.DataArray(
                 unicode_var, coords=[time1], dims=["time"]
             ).astype(np.unicode_),
+            "datetime_var": xr.DataArray(datetime_var, coords=[time1], dims=["time"]),
+            "bool_var": xr.DataArray(bool_var, coords=[time1], dims=["time"]),
         }
     )
 
@@ -118,6 +128,10 @@ def create_append_test_data(seed=None):
             "unicode_var": xr.DataArray(
                 unicode_var[:nt2], coords=[time2], dims=["time"]
             ).astype(np.unicode_),
+            "datetime_var": xr.DataArray(
+                datetime_var_to_append, coords=[time2], dims=["time"]
+            ),
+            "bool_var": xr.DataArray(bool_var_to_append, coords=[time2], dims=["time"]),
         }
     )