In this paper, the proposed yield function is the function of stress, hardening parameter, and strain rate. To fully describe the stress state and strain rate condition of material during dynamic loading, a new coordinate system, which is composed of a stress axis and strain rate axis, is employed to present the proposed rate-dependent yield surface. The strain rate is regarded as a variable in applying the consistency condition. The rate-dependent consistency is satisfied strictly during the whole dynamic loading. The nonassociated flow rule is employed to describe the dilatancy behavior of concrete. The loading–unloading criterion based on Ilyushin’s postulate is developed into the rate-dependent loading–unloading criterion that can consider reasonably the change of elastic domain caused by strain rate. Furthermore, a three-dimensional (3D) dynamic elastoplastic model of concrete is established within the framework of the rate-dependent consistency condition. Under the dynamic uniaxial compression loading condition, the model characteristics related to rate-dependent consistency condition are discussed and analyzed. Five sets of dynamic experiment results of concrete are employed to evaluate the performance of the model.