This paper presents the elastic analysis of a rotating sandwich solid disk composed of three-layered perfectly-bonded composites. The center and outer regions of the solid disk are two homogeneous isotropic media, and the middle region is a transition zone made of functionally graded materials (FGM). Two cases are considered. One is on FGM with power-law gradient. For this case, explicit expressions for full elastic fields are derived. The other is on FGM with any radial nonhomogeneity, for which an analytic approach is proposed to reduce the problem into a Fredholm integral equation. The validity of the latter method is ensured by comparing numerical results of the elastic fields with the exact ones for the case of power-law gradient. For a general case, the current study presents the influences of the gradient, width variation of the FGM, and rotational velocity on the distribution of the radial and hoop stresses for a rotating composite disk made of aluminum and zirconia. The method presented in this paper may help engineering designers in choosing appropriate gradients and materials to acquire the optimal state of a rotating functionally graded disk.