［Purposes］ As for the valuation of American options under regime-switching Kou’s jump-diffusion processes. ［Methods］ Based on the linear complementarity problem discretized by Crank Nicolson fitted finite volume method, an efficient modulus matrix splitting iterative method is introduced to solve it. ［Findings］ The convergence theorem of the algorithms are given under the H+-matrix property of the discrete matrix. ［Conclusions］ Numerical experiments verify the effectiveness, robustness and convergence of the new method, and the computational efficiency of themodulus-based matrix splitting iteration methods is superior to the projected successive overrelaxation iteration method.