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Used the staggered grid techniques to translate the velocity derivative with respect to time into stress derivative of spatial in velocity-stress equation, and expressed the elastic wave equation in first-order velocity-stress equation equial to second-order hyperbolic equation, the simulation for the three dimensional tricomponent of seismic wave field is achieved. The analysis of wave field snap shoot, VSP image recording and ground image recording indicates that the obvious quasi-P, quasi-SV and quasi-SH, and even some particular phenomena produced in azimuthal anisotropic medium propagating of earthquake wave such as shear-wave splitting, shear-wave splitting dead zone and wave-front three bifurcation exist in wave field image. The results show that three dimensional simulation of staggered grid technique is an important comp lement for study of the inversion of azimuthal of anisotropic medium to earthquake wave propagation in azimuthal anisotropic medium.