Recently, fractional partial differential equations have been widely applied in option pricing problems, which better explains many important empirical facts of financial markets, but rare paper considers the multi-state options pricing problem based on fractional diffusion models. Thus, multi-state European option pricing problem under regime-switching tempered fractional partial differential equation is considered in this paper. Due to the expensive computational cost caused by the implicit finite difference scheme, a novel implicit-explicit finite difference scheme has been developed with consistency, stability, and convergence guarantee. Since the resulting coefficient matrix equals to the direct sum of several Toeplitz matrices, a preconditioned direct method has been proposed with O(S̄ Nlog N+ S̄ N) operation cost on each time level with adaptability analysis, where S̄ is the number of states and N is the number of grid points. Related numerical experiments including an empirical example have been presented to demonstrate the effectiveness and accuracy of the proposed numerical method.