Abstract: To achieve the strength criteria under one-dimensional strain condition for a kind of carbon fiber two-dimensional orthogonal plain woven reinforced polymer matrix composite, formulas were proposed to describe the strain rate-dependent stress-strain relationships in its three principal directions respectively, according to just completed quasistatic and dynamic compression experiments. Then the relationships between strain rate and initial yield strength or compression failure strength for the composite were demonstrated. Based on the results, the strain rate-dependent Tsai-Hill yield and failure criteria under one-dimensional strain condition were achieved. The variation of the Tsai-Hill yield and failure criteria with increasing strain rate was computationally obtained. Results show the strength properties of the researched composite are related to strain rate, and the strain rate effects are anisotropic.