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This paper studies decoupled numerical methods for a mixed Stokes/Darcy model for coupling fluid and porous media flows. A two-level algorithm is proposed and analyzed in Mu and Xu (2007) [10]. We generalize the two-level algorithm to a multilevel algorithm in this paper and present numerical analysis on the error estimates for the multilevel algorithm. The multilevel algorithm solves the mixed Stokes/Darcy system by applying efficient legacy code for single model solvers to solve two decoupled Stokes and Darcy subproblems on all the subsequently refined meshes, except for a much smaller global problem only on a very coarse initial mesh. Numerical experiments are conducted for both the two-level and multilevel algorithms to illustrate their effectiveness and efficiency, and validate the related theoretical analysis.