The residual stresses induced in fiber-reinforced functionally graded composites cooling down from the processing temperature are determined with concentric cylinder model and analytical solutions of inhomogeneous governing equations for displacement components, which include particular solution and general solution of the corresponding homogeneous equations. The analytical solutions presented here are general for power-law variations of the elastic moduli of the functionally graded matrix. With a power exponent, analytical expressions for the residual stresses of fiber-reinforced functionally graded composites can be obtained. By changing the power exponent and the coefficient of the power terms, the solutions obtained here could be applied to fiber-reinforced functionally graded composites with different properties. The results show that the large difference exists between functionally graded composites and common-used composites consisting of two phases of homogenous materials. The variation of matrix modulus and fiber percentage have a great deal of effects on the residual stresses in functionally graded composites.