The first-principle with pseudopotentials method based on the Density Functional Theory（DFT）was applied to calculate the lattice parameter，total energy and volume，bond length，density，bulk modulus（B）of primitive cell of the single spinel nitrides γ-A3N4（A：C、Si、Ge、Sn（Group IVB）and discussed to gap energy，static dielectric constant ε（0）and optical absorption peak. Results of calculation are still in excellent agreement with the experimental values. To γ-A3N4（A：C、Si、Ge、Sn（Group IVB），in calculation bulk modulus，LDA was excellent than GGA，but GGA provided a more adequate description of the structural properties and energy of the system than LDA. In this paper, except γ-Sn3N4，the First-Principle can accurately calculate the system of γ-C3N4，γ-Si3N4 and γ-Ge3N4.