Abstract: In practical engineering, the concrete structures are usually subjected to an initial static load before dynamic loading. Most previous studies on the strain rate effect of concrete do not consider the influence of initial static load on the dynamic strength, which leads to the computed results of dynamic strength larger than the actual value. Therefore the structural designed by these methods is unsafe. Based on the mechanism analysis of concrete rate effect under staticdynamic coupled loading, a clear definition of initial static load was given by authors. Then, the relationship of concrete material parameters with the initial static load and the strain rate was derived. And, a general method for static-dynamic coupled strength criterion was proposed. The combination influence of initial static load and strain rate on concrete strength is reflected by the strength parameter. The static-dynamic strength of concrete is consist of the initial static load, the dynamic cohesive strength and the frictional strength. Then a static-dynamic coupled multiaxial strength criterion of concrete was established by combining the obtained concrete material parameters with nonlinear dynamic multiaxial strength criterion. The strength surface of the present strength criterion expands outward with the increase of strain rate under the same initial static load, while contracts inward with the increase of initial static load under the same strain rate. In another word, the strength of concrete increases with the increase of strain rate at the same initial static load, and decreases with the increase of initial static load at the same strain rate. Moreover, when the initial static load and the strain rate are invariable, the strength surface of this criterion is determined, and the loading path has no influence on the strain rate effect of concrete, but the hydrostatic pressure effect is influenced by the loading path. Thus, the strength of concrete at different loading path is different due to the various hydrostatic pressure effect. Finally, the established criterion was verified based on the static and dynamic combined strength test results of concrete.