Q345-TA2 titanium-steel clad plate, because of its high strength and excellent corrosion resistance , has been more and more used in dynamic environment. In this paper, Applying the GLeeble - 3500 thermal simulation testing machine and split hopkinson pressure bar (SHPB) device, the quasi-static and high –strain- rate compression were carried out. The experimental results show that the Q345 - TA2 titanium-steel composite material has enhanced effect of strain rate, plasticizing effect and softening action of adiabatic temperature rise, but not very sensitive to strain rate change within the scope of the each partition of quasistatic and dynamic. Based on the considering of the adiabatic temperature rise, modifying the jaynes-cummings constitutive model, the fitting obtained can be used to analyze structure under the action of impact load of the material constitutive model, the results are good.