This article discussed the problem of reliability-based topology optimization design (RBTO), combined evolutionary structural optimization (ESO) and the reliability analysis method based on the stochastic finite element method (perturbation), established the mathematical model of reliability-based topology optimization design. The reliability constraint is taken as a global constraint. The stochastic perturbation method is used to solve the reliability to transform the implicitly bound constraints into explicit. The evolutionary structural optimization method is extracted for topology optimization design. The flow chart of reliabilitybased topology optimization design is showed. Several examples are given to verify the method and the results indicated the method is feasible. It provided the theory basis for the project application.