Three-dimensional periodic finite element models of unidirectional composites and phenolic resin matrix two dimensional woven composite laminates are established. The periodical boundary conditions are applied to the finite element method (FEM) analysis of the two models to ensure stress continuous and strain continuous on boundary surfaces. The mechanical parameters of unidirectional composites are obtained by FEM analysis. The tensile, compression and shear progressive damage analysis of the laminates are simulated at normal temperature and when the modulus of phenolic resin is changed at the low temperature of -50 ℃. Appropriate criterions are chosen to predict the failure process of the laminates. The tensile, compression and shear tests are conducted at normal temperature and the low temperature of -50 ℃ of the two-imensional woven composite. The FEM results are compared with the experimental results to acquire the factors affecting the mechanical properties of phenolic resin matrix composite laminates at low temperature。The results prove that the mechanical properties of the composite at low temperature are better than those at normal temperature, verifying the correctness of the analysis method by the test.