The fast multipole method (FMM) is an O(N) solver of a full linear system appearing in integral equation methods, for example, surface charge simulation method (SCM) and boundary element method (BEM). An effective preconditioning technique for the FMM, which employs a nested FMM having intentionally deteriorated precision, was proposed and applied to the FMM-SCM and FMM-BEM using the Bi-CGSTAB2. In this paper, this technique called minor iterative preconditioning is applied to the FMM-SCM using the GMRES in order to solve electrostatic field calculation problems. The comparison of CPU times and convergence properties with those by some variants confirms good acceleration performance of the utilized technique.