Wavefront distortion affects the compressibility and the far-field focal spot quality of the output laser pulse of parallel grating pair compressor. We establish a theoretical model of parallel grating pair compressor based on ray-tracing method and principle of Fraunhofer far-field diffraction, and analyze the effects of wavefront error of input pulse, the deformation and wave aberration of grating diffraction surface on the spatial-temporal property of the far-field focal plane of the compressor output pulse. The corresponding error tolerances are presented based on Monte-Carlo simulation. The results provide a theoretical reference of wavefront distortion correction and grating quality control for parallel grating pair compressor in high-power laser facilities.