The present study has advanced our previous fiber-based simulation technique to deal with matrix nonlinearity for the micromechanical analysis of fiber-reinforced composites. We focused on the evaluation of compressive strength of composites in relation to fiber orientation, using three-dimensional micromechanical analyses. For this purpose, the effect of fiber orientation on composite elastic modulus was verified through comparison with theoretical models, and the effect of matrix nonlinearity was also validated. The present fiber-based simulation with matrix nonlinearity was applied to evaluating the effect on compressive strength of composites consisting of plies having different orientation angles, and a microscopic effect near the ply interface on the compressive strength was discussed.