Suppose I am having this object objectDemo which calls to the method objectDemoMethod with 2 parameters String and null.
The error message you are getting is expected since you are using argument matcher for only one argument and not the other. From Matchers Javadoc:
If you are using argument matchers, all arguments have to be provided by matchers.
Therefore, the fix is to use a matcher for the second parameter of the method as well. In this case, it would be a matcher matching null. Depending on the version of Mockito and Java, you can have:
Starting with Mockito 2, you can use ArgumentMatchers.isNull(). This works with Java 8 and above:
verify(objectDemo, times(1)).objectDemoMethod(any(String.class), isNull());
Note that if you're running with Java 7 or older, you'll need an explicit cast to make this work, because the type inference in those versions of Java does not take into account the types of the method called:
verify(objectDemo, times(1)).objectDemoMethod(any(String.class), (String) isNull());
If you're using Mockito 1, you can use the Matchers.isNull(clazz) instead:
verify(objectDemo, times(1)).objectDemoMethod(any(String.class), isNull(String.class));
For the Java ≤ 7 or Mockito 1 cases, the examples uses a case where the second parameter was of type String: it would need to be replaced with the actual type of the method parameter.