Abstract: Using the theoretical model of pulsed beam through gra ting pair in the case of finite beam size and starting from the Fourier angle spectrum of the pulsed beam,the spatial and temporal properties of the pulsed super-Gaussian beam single and double passing compressor and the effects of high-order dispersion are studied.It's found that when the pulsed super-Gaussian beam once passes through the grating pair,the time-dependent spatial shift will be introduced in the output pulse by the transverse spectrum shift,but the effect will be eliminated when twice passes and that high-order dispersion affects the spatial and temporal properties of the output pulse,causes the pulse front distortion and induces space-time aberration in the output pulse.