Mid-long term voltage stability refers to voltage stability concerning the dynamics of the slow dynamic elements and protection devices in power systems. To improve the mid-long term voltage stability, this paper proposes a scheme of model predictive control (MPC) based on Galerkin method. The basic principle of MPC is to solve the optimization problem regarding voltage stability control based on the prediction model periodically. By applying the optimal control scheme to power systems, the mid-long term voltage stability can be enhanced. The Galerkin method-based polynomial approximation approximates the relationship between mid-long term trajectories and control parameters by a polynomial function. The polynomial function acts as a prediction model to predict future system trajectories under different values of control parameters in MPC. The advantage of the proposed method is that its prediction accuracy is relatively high and thus the control efficiency of MPC is improved, as the polynomial function can embody the non-linear characteristics of the power system. In the case study, the 3-machine 10-bus system and the New England 39-bus system are taken as examples to compare the MPC based on the proposed method and the trajectory sensitivity method in terms of prediction accuracy, computation time and control results.