In this paper, a quasi-max-min predictive control(QMM-MPC) algorithm based on depth information is proposed for visual docking of the 6-DOF autonomous underwater vehicle(AUV), which can effectively improve the performance of the complex underwater visual servo docking system. Firstly, a new 6-DOF visual servo model for the underwater AUV is established to solve the problem of the uncertainty of depth information caused by the low visual visibility of the underwater AUV. Then, an online depth estimator is designed by combining the measurement data of AUV motion and image feature motion. Meanwhile, a QMM-MPC algorithm combining multi-Lyapunov functions is proposed, which can reduce the strong conservatism caused by one upper bound of the Lyapunov function in the traditional QMM-MPC algorithm by solving the different upper bound of each vertex in the convex polyhedron. Finally, the simulation results show the effectiveness of the proposed algorithm.