We developed a multistep thermodynamicperturbation method to compute the interfacial free energies by nonequilibrium work measurements with cleaving potential procedure. Using this method, we calculated the interfacial free energies of different crystal orientations for the Lennard-Jones system. Our results are in good agreement with the results by thermodynamic integration method. Compared with thermodynamic integration method, the multistep thermodynamicperturbation method is more efficient. For each stage of the cleaving process, only a few thermodynamic perturbation steps are needed, and there is no requirement on the reversibility of the path.