Due to the characteristic of the rate sensitive material, the changing mechanism of strength and stiffness of concrete structure under various strain rates are different. In addition to the complex stress state where concrete structure is subjected to dynamic loading such as earthquake, the effect of the strain rate is an important factor that can not be ignored. If projects are designed and calculated with strength theories of uniaxial tension, compression and shear, there will have great potential dangers in the construction and use of structure. Based on the Ottosen criterion model, in the present paper, by analysis of multiaxial static and dynamic strength test data of numerous concrete specimens, which are classified into different strength grades, a multiaxial dynamic strength criterion is reasonably established, in which both the strain rate effect and the strength of concrete are taken into account. The analysis results show that the predicted strength of the failure criterion is in good agreement with the basic requirements of continuity, smoothness and convexity and better reflects the dynamic strength change rule of ordinary concrete. Meanwhile, the strength criterion can be obtained just by the typical stress points, thus it has a simple expression form and is convenient for practical application to analysis of engineering structures.