We provide detailed analytical expressions of group-delay dispersion and three-order dispersion for reflection grism-pair using angle dispersion and material dispersion. The dispersion formulas obtained in this study are consistent with the results of the ray-tracing method. The analytical expressions can be used to design a grism-pair for compensating for the dispersive material. Furthermore, the dispersion performances of the grism pair depending on structural parameters and temperature are comprehensively analyzed. The results show that the parameters have a large influence on the dispersion of grism, such as incidence angle, grating constant, and apex angle of the prism. To compensate for material dispersion of amplifying medium, we can adjust the above parameters to obtain group delay dispersion and third order dispersion.