Abstract: TTI qP wave numerical simulation method is more accurate than VTI qP wave numerical simulation method in describing the propagation law of seismic wavefield in anisotropic medium because of considering the dip angle factor.Using the pseudo acoustic wave equation,the authors carried out high order finite difference numerical simulation of the seismic wavefield in the TTI medium in this paper.After improving the distribution of the attenuation function,the authors used the improved perfectly matched layer (PML) boundary control equation to deal with the wavefield boundary and achieved good results.Then the pseudo shear wave in the numerical simulation of pseudo acoustic wave equation was suppressed and the stability problem was analyzed.The numerical simulation of different models prove that the TTI medium pseudo acoustic wave equation is stable and the PML boundary control equations have high reliability and applicability.