A new reflective grism, which combines together the grating and prism, is introduced in this paper. The numerical simulation, based on the ray tracing, shows that the grism pair can introduce minus GVD and GDD; therefore it can well compensate for the material dispersions in the chirped pulse amplifier (CPA). Compared to the conventional CPA with up-chirp, the new scheme with down-chirp can support a near Fourier Transform-limited compressed pulse due to much better compensation for high-order dispersion of materials in amplifier, in which the grism acts as the stretcher and the ZF7 bulk material as the compressor. In addition, the improved transmission efficiency and simplified configuration makes it a promising way to amplify femtosecond laser pulses to sub-mJ at a high repetition rate.