Concrete is prone to damage under explosive loads, which can cause a large number of casualties and property losses. The concrete fragmentation process during explosion is transient and dynamic, and the experimental measurement of such events is difficult and risky to conduct, and the intermediate explosion process is difficult to observe in the experimental tests. Therefore, the numerical simulation is an ideal method to model and simulate the explosion process of concrete. Different from the traditional finite element method, Peridynamics (PD) method uses the spatial integral equation to replace the traditional local differential equation to solve the fragmentation problem with massive and complex discontinuous patterns. In this study, a peridynamics (PD) model is developed to simulate the failure process of reinforced concrete (RC) structures under radial blasting. Concrete PD models with different cavity sizes and reinforcement conditions were established and calibrated with the experimental data. We find that the crack growth and damage pattern obtained in the peridynamics simulation is consistent with the experiment test results, which verifies the feasibility of peridynamics method as a modeling tool for modeling concrete damage under explosive load and for evaluating anti-explosion performance of RC concrete structures.