The quasi-static and dynamic compression properties of carbon fiber-reinforced phenolic composite are investigated by a series of MTS and SHPB tests. The results show that the material is rate-dependent and temperature-dependent. A new nonlinear viscoelastic constitutive model is proposed and the coefficients in the constitutive equation are obtained by the experiment stress-strain curves. The influence of temperature on the constitutive equation is remarkable, and its effects can be described by the material parameters related to temperature. Based on the consideration that the responses of the material to reducing strain rate and raising temperature are similar, the time-temperature equivalent law is investigaled and the corresponding equivalent curve under different loading conditions is approached.