Summary: In this study, we introduce a rapid iterative algorithm to find a common element of the solution set of split variational inclusion problems and the set of fixed points of a nonexpansive mapping by using the hybrid steepest descent method. The strong convergence results of presented algorithms have been obtained under some mild conditions. The proposed results are the supplement, extension and generalization of the previously known results in this area. Finally, preliminary numerical results indicate the feasibility and efficiency of the proposed methods.