This paper presents a structural non-probabilistic reliability analysis approach based on a hybrid algorithm of the simulated annealing-particle swarm optimization algorithm and the differential evolution (SAPSO-DE) algorithm. In the structural non-probabilistic reliability analysis, the problem with uncertain parameters can be formulated as an optimization problem using convex model. However, the limit state function is usually implicit for the uncertain parameters. By employing the SAPSO-DE hybrid algorithm based on the evolution of the cognitive and social experiences, the problem of the structural non-probabilistic reliability analysis is solved. A numerical example is given to illustrate the high precision and good feasibility of the present method. The results shows that this proposed approach is effective, and has the predominant capability of global optimization and convergence precision.