The true triaxial compression tests under different stress ratios and different loading rates are conducted to study the static and dynamic mechanical properties of concrete structures under complex stress conditions. The variations of concrete’s compressive strength and deformation characteristics are examined in depth. Based on the octahedral stress space, the true triaxial dynamic failure criterion of the concrete considering the rate effect is established. The results show that the ultimate compressive strength of concrete under true triaxial compression increases with the increase of stress ratio. At lower stress ratio, the ultimate compressive strength of concrete gradually increases with the increase of strain rate; at higher stress ratio, the ultimate compressive strength of concrete decreases firstly and then increases. The deformation on the lateral compression surface changes from compression failure to tensile failure in a shorter time with the increasing strain rate, and the deformation becomes smaller and smaller in the direction of greater lateral pressure with the increasing strain ratio. The expression of the true triaxial dynamic failure criterion based on the octahedral stress space contains three rate-effect parameters, which is verified to be in good agreement with the experimental data.