Accurate structural analyses of continuous fiber-reinforced polymers (FRPs) are imperative for diverse engineering applications, demanding efficient material constitutive models. Nonetheless, the constitutive modeling of FRPs is complicated by the nonlinear behavior resulting from internal damages and the inherent plasticity. Consequently, this study presents an innovative anisotropic constitutive model for FRPs, designed to adeptly capture both the damage evolution and plasticity. All requisite parameters can be easily obtained through fundamental mechanical tests, rendering the model practical and user-friendly. The model utilizes the three-dimensional Puck criteria to determine damages, initiating the evolution process through a combination of continuum damage mechanics and linear stiffness attenuation methods. This evolution is coupled with a one-parameter plastic model. Subsequently, the numerical implementation method, integrated into ANSYS, is detailed. This emphasizes the Cauchy stress and consistent tangent stiffness solution strategy. Finally, the effectiveness of the developed model is demonstrated through comprehensive verification, encompassing existing biaxial tension and open-hole-tension tests conducted on carbon and glass FRP laminates. The simulation results exhibit a remarkable correspondence with the experimental data, validating the reliability and accuracy of the proposed model.