How can I mock private static method with PowerMockito?

If anotherMethod() takes any argument as anotherMethod(parameter), the correct invocation of the method will be:

PowerMockito.doReturn("abc").when(Util.class, "anotherMethod", parameter);

To to this, you can use PowerMockito.spy(...) and PowerMockito.doReturn(...).

Moreover, you have to specify the PowerMock runner at your test class, and prepare the class for testing, as follows:

@PrepareForTest(Util.class)
@RunWith(PowerMockRunner.class)
public class UtilTest {

   @Test
   public void testMethod() throws Exception {
      PowerMockito.spy(Util.class);
      PowerMockito.doReturn("abc").when(Util.class, "anotherMethod");

      String retrieved = Util.method();

      Assert.assertNotNull(retrieved);
      Assert.assertEquals(retrieved, "abc");
   }
}

Hope it helps you.