Compared with VTI qP-wave modeling,TTI qP-wave numerical simulation method which considers dip angle factor could be more accurate in describing the characteristics of wave-field propagation in real anisotropic media.Because of the rapid change of dip angle in TTI media,using the conventional acoustic approximated method may cause numerical instability.In this paper,the authors first derived the stable TTI second-order qP-wave equations by introducing an anisotropic control parameter to ensure the stability of qP-wave propagation.Then,the equivalent first-order stress-velocity forms were deduced through introducing the pseudo-velocity components of the wave-fields,and the corresponding PML boundary condition was given.Finally,the authors implemented accurate numerical simulation using the optimal rotated stagger-grid finite-difference (RSGFD) method.Numerical results demonstrate that TTI first-order qP-wave equations can describe the kinematics features of qP-wave effectively and stably,and the application of optimal RSGFD method can acquire accurate synthetic seismic recordings and enhance computational efficiency relatively.