The mechanical properties of unidirectional fiber-reinforced plastic (UD-FRP) are affected by a variety of micro-defects, such as random fiber arrangement, fiber misalignment and micro-voids. This study aims to investigate how these multiple micro-defects interact with each other and how they affect the strength and failure mechanisms of UD-FRP by means of computational micromechanics. The composite behavior was simulated by the finite element analysis of a representative volume element of the composite microstructure in which the random distribution of fibers, the micro-voids, and the fiber misalignment are explicitly included. Both matrix and interface failure were considered for the loadings of transverse tension/compression, longitudinal compression, transverse/ longitudinal shear, and their combination. It was found that these three micro-defects significantly weakened the compressive strength of UD-FRP along the longitudinal direction. Especially, the fiber misalignment magnified the effect of fiber arrangement, while the micro-voids reduce the effect. Besides, the fiber arrangement and micro-voids significantly weakened the tensile and compressive strength of UD-FRP along the transverse direction, but their interaction effect was not obvious. Moreover, transverse and longitudinal shear strength are significantly affected by micro-voids, but only longitudinal shear is affected by geometric fiber arrangement, and this effect is also weakened by micro-voids. Finally, the damage envelope under the combined longitudinal compression and transverse loads was obtained and compared with the Tsai-Wu failure criterion. The results showed that the Tsai-Wu criteria can provide an effective estimation for the failure locus under this biaxial loading condition