Abstract: It is still a challenging problem to establish a constitutive model for cyclic plasticity and reveal its microscopic mechanism. A cyclic plasticity-damage model was proposed in this study to predict the stress-strain response of fiber reinforced polymer under cyclic loading. This model is a further extension of the elastic-plastic constitutive model to describe the nonlinear hysteresis behavior proposed by the authors. It can predict the nonlinear responses during loading, hysteresis behavior during unloading and reloading and the ratcheting phenomena under a large number of cycles. As a benchmark problem verification, the experimental data by Kawai et al, were compared with the numerical prediction of the model in this paper. The results show that the model can simulate the ratcheting behavior of carbon fiber/epoxy unidirectional composite under off-axis cyclic loading.