A more comprehensive theoretical model to deal with the pulsed beam through grating pair is obtained and used to study the spatial and temporal properties of the pulsed Gaussian beam single and double passing compressor and the effects of high-order dispersion. It is found that when the uncollimated input beam single passes through compressor, the time-dependent spatial shift will be introduced in the output pulse, and the duration of the output pulse will depends on the position of the beam waist. In addition, Furthermore, for the single-passed compressor, the third-order dispersion causes the pulse front distortion, and the fourth-order dispersion leads to the time-depended spatial shift in the output pulse.