The structural and electronic properties of graphene/graphene-like Aluminum Nitrides monolayer (Gr/g-AlN) heterojunction with and without vacancies are systematically investigated by first-principles calculation. The results prove that Gr/g-AlN with nitrogen-vacancy (Gr/g-AlN-VN) is energy favorable with the smallest sublayer distance and binding energy. Gr/g-AlN-VN is nonmagnetic, like that in the pristine Gr/g-AlN structure, but it is different from the situation of g-AlN-VN, where a magnetic moment of 1 μB is observed. The metallic graphene acts as an electron acceptor in the Gr/g-AlN-VN and donor in Gr/g-AlN and Gr/g-AlN-VAl contacts. Schottky barrier height Φ B , n by traditional (hybrid) functional of Gr/g-AlN, Gr/g-AlN-VAl, and Gr/g-AlN-VN are calculated as 2.35 (3.69), 2.77 (3.23), and 1.10 (0.98) eV, respectively, showing that vacancies can effectively modulate the Schottky barrier height. Additionally, the biaxial strain engineering is conducted to modulate the heterojunction contact properties. The pristine Gr/g-AlN, which is a p-type Schottky contact under strain-free condition, would transform to an n-type contact when 10% compressive strain is applied. Ohmic contact is formed under a larger tensile strain. Furthermore, 7.5% tensile strain would tune the Gr/g-AlN-VN from n-type to p-type contact. These plentiful tunable natures would provide valuable guidance in fabricating nanoelectronics devices based on Gr/g-AlN heterojunctions.