Abstract: A micromechanical representative volume element (RVE) model was developed for analyzing effective mechanical behaviors of continuous bidirectional-fiber-reinforced matrix composites (CBFRCs) by combining the homogenization method and finite element method. In the proposed RVE model, the imperfect interfaces between the fiber and the matrix were taken into account by introducing some cohesive contact surfaces. The results show that an imperfect interface with a different interfacial stiffness may induce different damage onsets in the matrix of CBFRCs. Compared with the interfacial fracture energy, both the interfacial stiffness and strength play a more important role in determining the out-of-plane tensile strength of the CBFRCs, while have slight effect on the in-plane tensile strength. The tensile strength of the CBFRCs will be reduced because of the existence of interface. With an increase in the fiber volume fraction, the in-plane tensile strength increases sharply while the out-of-plane tensile strength decreases slightly. The numerical results indicate that the proposed model is simple and efficient for performing realistic optimum design on complex three dimensional fiber-reinforced composites.