Aiming to constrained visual servoing systems of mobile robots, this paper proposes a quasi-min-max model predictive control(MPC) scheme for visual servoing stabilization of mobile robots. Based on visual servoing error models of mobile robots, a linear parameter varying(LPV) predictive model is presented for visual servoing of the mobile robot. Then by introducing the min-max strategy, the model predictive controller is designed for visual serving stabilization of mobile robots. Comparing to the traditional visual servoing predictive controllers, the presented controller is obtained by only solving the convex optimization problem formulated by linear matrix inequalities, which decreases the computational demand of the visual servoing predictive controller and guarantees the asymptotic stability of the closed-loop visual servoing system. The simulation results verify the effectiveness of the proposed scheme and its merits in terms of the computational efficiency.