We have proposed a new concept for solid insulation; an application of FGM (Functionally Graded Materials). By controlling the distribution of dielectric permittivity inside solid insulators, we can achieve the efficient field control with keeping simple configuration of solid insulators.In this paper, we described a computer-aided optimization technique for the FGM solid insulators. By controlling the filler particle concentration in the matrix, an optimized field distribution is obtained. From the calculation results, we confirmed that the proposed optimization method could obtain novel distributions of permittivity, which have the highest performance of the field control effect. Finally, we could confirm the significant effect of FGM application for gas / solid composite insulation system.