[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.