Peridynamics is a recently developed meshfree method with many aspects needing to be further studied, such as viscoelasticity, plasticity and the coupling of elasticity, plasticity and viscosity. The analytical ability for considering viscoelastic behavior of peridynamics is developed. The theoretical basis, modeling procedure and numerical scheme of peridynamics are first reviewed. Then the expressions of creep compliance under different stresses and the peridynamic creep response functions are deduced combing time-stress equivalence principle of nonlinear viscoelastic materials and utilizing Burgers viscoelastic model. In this manner, the peridynamic creep simulation method which can be applied to polymer bonded explosives is established. The creep behavior of PBX9502 is then simulated using this method, which indicates a good conformity with experiment results. The established method can be applied to analyze creep behavior of polymer bonded explosives under different temperatures and different stresses.