As a kind of traditional optical components, prisms are limited in the application of modern optical instruments because of their nonlinear dispersion. By analyzing the dispersion nature of prisms, a dispersion model of material was established and a design method of compound prisms with linear dispersion was proposed. Two kinds of materials with close nonlinear dispersion coefficients T1 and T2 and different linear dispersion coefficient V were used. By controlling the parameters of the compound prism and the incident angle, linear dispersion could be achieved. Finally, the evaluation index was established for the linear dispersion compound prism. The designed result was evaluated scientifically and reasonably. The correctness of the design theory was verified. It was found that the nonlinear dispersion of the compound prism was improved effectively. The improvement of nonlinear dispersion was dependent on the absolute nonlinear coefficient P of two kinds of materials. When $P$ was greater than 0.01, the compound prism could achieve linear dispersion. The nonlinear (NL) of the dispersion curve was better than 5%.