On the basis of the vector diffraction theory, the equation o f two_dimensional grating in arbitrary angle of incidence is given, the complet e analytical form of angular dispersion formula of two_dimensional grating is f irst ly deduced, and the concept of angular dispersion of diffractive polar angle (AD DPA)(the first kind angular dispersion) and angular dispersion of diffractive az imuthal angle (ADDAA) (the second kind angular dispersion) are established. In addition, according to theoretical analysis and numerical method on ADDPA and AD DAA of two_dimensional grating, the mechanism that diffraction spot array gener at es distortion is explained when the incidence wave has an angular deviation from the grating normal. Moreover, the conditions for causing mutation of ADDAA and l eading to the dramatic change of diffraction spot array are also determined. Thi s work, therefore, is of great importance in basic theory research. In practical ap plication, taking x_ray diffraction, low_energy electron diffraction and reflect ion high_energy electron diffraction of crystal and quantum d ot for example, we may take advantage of the above formula to test, analyz e and explain the structure of a crystal lattice and the crystal growth process, then we can find new methods of characterizing crystal structure.