In this paper, the analytic solution of Robust Model Predictive Control (RMPC) with an ellipsoidal disturbance set is presented. Compared to the conventional polyhedron disturbance set, a few explicit expressions could be obtained, such as a constraint handling variable and a minimal robustly invariant set. In addition, the specific structure of the ellipsoidal disturbance set simplifies the optimization procedure with the min-max approach. Therefore, the computational time could be reduced by reformulating the disturbance vector to a known expression. The resulting formulation is a class of quasi-convex program, and an efficient solver can be used to solve such an optimization problem. Simple simulation examples for both nominal cost control and worst-case cost control are represented.