Third- and fourth-order dispersions (TOD&FOD) are unavoidable effects in ultra-short chirped pulse amplifier (CPA) systems which can greatly disturb the output pulse shape. Grism- pairs (grating+prism) compressors are currently used for the TOD compensation in CPA systems.  In this work the Genetic algorithm optimization method has been used to design an optimal grism-pair compressor with the ability of simultaneous compensation of TOD and FOD of a typical CPA system. Results show a significant reduction in the output pulse peak power by the optimal design of grism-pair compressor.