The physical model of ultra-short laser pulse propagation during quasi-phase matched crystal is built and modified nonlinear Schrdinger equation is solved with step Fourier method. The temporal and spatial characteristics of femto-second laser pulse propagation in periodically poled lithium niobate (PPLN) crystal are achieved numerically. It is found that when the fundamental power is beyond the critical power, temporal splitting and spatial focusing of pulse are induced by self-focusing effect. Temporal splitting results in pulse width decrease with the increment of propagation distance, and minimal width is obtained at the focal point. On the other hand, spatial focusing brings decrement of focused diameter with the increment of propagation distance, and minimal diameter is obtained at the focal point and then diffused outward. Finally, the peak intensity of the pulse reaches maximal value at the focal point, and then reduces gradually. The length of quasi-phase matched crystal is restricted by self-focusing effect during ultra-short laser frequency doubling process.