Abstract: Starting from unstable phase-shift formula of wavefield continuation and based on the perturbation theory which is usually used in the solving of inverse question,we derived a high-order form of wave equation generalized screen pre-stack depth migration operator equation by utilizing gradual spreading of single square root operators.Aiming at the instability for the calculation items of scattered wavefield in lateral variable-velocity media,we proposed an effective way to improve the stability by math approximation,and applied it to the wavefield recursion extrapolation.Then a stable seismic migration imaging method of high precision screen operators was obtained.The numerical testing and actual data processing results show that the method has higher precision,which is better for the imaging of wide-angle information,and is the effective supplement and development of traditional generalized screen operators.