In this study, elastic properties of the plain-weave fabric composite laminates are investigated through finite element analysis. In the analysis, the intra-lamina inhomogeneity caused by the architecture of woven yarns is taken into consideration. Using the homogenization procedure, the effective plate stiffness of the fabric composite laminate is calculated. Assuming the number of laminated plies is infinite, the effective three-dimensional continuum elastic properties of the fabric composite are also calculated. Then, the effect of the number of plies on the in-plane (in-plane tension and in-plane shear) elastic properties and out-of-plane (bending and twisting) elastic properties of the composite laminate is investigated. Through the numerical investigation, it is found that the inplane tensile stiffness and the twisting stiffness of the composite laminate are overestimated, particularly for a small number of laminated plies, when they are evaluated with the assumption that each lamina is homogeneous with the effective three-dimensional continuum elastic properties.