In order to understand the dynamic strength properties of the concrete under complex stress state, a united multiaxial static-dynamic strength criterion is established in the octahedral stress space in which the strain rate effect is considered. The failure surface of the proposed model in three-dimensional (3D) stresses space is represented by a quadratic function. The strength envelope in the deviatoric plane is described by an elliptic curve similar to that of Willam-Warnke model, and the tensile and compressive meridians are calibrated using typical stress points method to consider the effect of the Lode angle on the dynamic strength. By the analysis of multiaxial static and dynamic strength test data of concrete, it is proved that the predicted strength of the failure criterion is in good agreement with the experimental data. Meanwhile, the strength criterion has simple expression form and is convenient for practical application.