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Detailed formulation of the detached-eddy simulation (DES) based on shear stress transport model (SST) was deduced.Based on finite volume method,detached-eddy simulation of supersonic turbulent flow over rearward facing step was conducted.Multi-block structured non-conform grid was designed.The obtained distribution of wall pressure coefficient along the downstream of the step was in good agreement with experiment.The structure of supersonic flow over rearward facing step is complicated and contains boundary layer-shock interaction,shock-shock interaction and secondary flow separation.The predictions of the corner pressure and location of the reattachment shock are more exact than the Reynolds-averaged method.Results show that detached-eddy simulation can simulate the supersonic separated flows exactly and has advantages over Reynolds-averaged method.The partition of the detached-eddy simulation can be easily achieved by using multi-block non-conform grid,which reduces the requirement of the computational resources as well.