Abstract: The axial compressive strength of carbon fiber reinforced polymer composites (CFRP) is significantly lower than the tensile strength, which hinders its wide applications. The failure mechanism of CFRP under unidirectional compression parallel to the fiber alignment direction is complex, but research on this issue is limited. In order to understand this mechanism more deeply and intuitively, a two-dimensional microscopic numerical model is proposed. The influences of various properties of the fiber and matrix on the compressive strength of CFRP are investigated, including the axial elastic modulus of the fiber (E_f1), the transverse elastic modulus of the fiber(E_f2), the shear modulus of the fiber (G_f12), the elastic modulus of the matrix (E_m), the proportional strength limit of the matrix (σ_p), the yield strength of the matrix (σ_s) and the degree of initial fiber misalignment. Results show that the model is capable of explaining the failure mechanism of CFRP under a unidirectional compressive load. Shear stress plays an important role in the compressive failure process. The localization of shear stress caused by initial fiber misalignment leads to plastic yield of the matrix and finally a kink band. Changes in these properties directly affect the concentration of shear stress in the defect areas, thereby affecting the compressive strength of the CFRP. When the values of E_f1, E_f2, G_f12,E_m, σ_p, σ_s are separately increased by 10% or the degree of initial fiber misalignment is decreased by 10%, the compressive strength of CFRP is increased by 2.33%, 0, 0.39%, 3.38%, 1.17%, 2.30% and 2.52% respectively. E_m has the greatest influence on the compressive strength of CFRP, followed by the initial fiber misalignment. The effects of the plastic properties of the matrix on the compressive strength of CFRP are obvious.