Macroscopic coefficients of thermal expansion of a composite material may depend upon both the geometry and the orientation of reinforcements containing in the material in addition to their elastic moduli and coefficients of thermal expansion. In the present study, general expression for macroscopic coefficients of thermal expansion of a composite material, in which many kinds of reinforcements with different aspect ratios and orientations are contained, are derived by using the equivalent inclusion method combined with the Mori-Tanaka theorem. In the analysis, the expression of the equivalent eigenstrain for each reinforcement is derived with respect to the local coordinate system based on its semi-axes and then it is transformed to the global coordinate system. Moreover, numerical calculation is performed to a flake-reinforced composite with a type of orientation distribution of the reinforcements. As a result, we found that a shear component of the macroscopic coefficients of thermal expansion of the composite is non-zero in value.