This article addresses robust model predictive control (MPC) for systems with polytopicdescription. An existing off-line robust MPC enables the on-line computation as simple assearching a state feedback gain among the look-up table. We consider enlarging the region ofattraction of the off-line MPC by incorporating free perturbation items. First, a largerellipsoidal region of attraction is off-line constructed, in which a simple optimization problemis solved on-line. Then, outside of this larger ellipsoid, a standard robust MPC is solved onlinesuch that the overall region of attraction can be rendered as a much larger nonellipsoidalone. The proposed approach possesses all the merits of the off-line MPC and greatly enlargesthe region of attraction. A simulation example is given to demonstrate the effectiveness.