Low frequency transmission system (LFTS) is a promising solution for offshore wind power integration. As a topology modified from the modular multilevel matrix converter (M3C), the hexagon converter(Hexverter) has some benefits in low frequency transmission. When Hexverter is applied to offshore wind power, the stochastic nature of renewable energy and its non-linear features make it hard for linear proportional integral (PI) control to reach desired control results. However, the Lyapunov function control strategy is better than PI control when applied to nonlinear systems. Therefore, this paper proposes a Lyapunov function control strategy based on Hexverter. Firstly, the global asymptotic stability of the Lyapunov function control strategy of Hexverter object is analyzed, and then the control law of the bilateral Lyapunov function control of Hexverter is derived based on the topology of Hexverter, and the parameter selection of Lyapunov function control is discussed. Finally, the Lyapunov function control system of Hexverter is constructed on MATLAB/Simulink and RT-LAB platforms to simulate the operation results under various working conditions, and by comparing the simulation results with PI control, the viability of the Lyapunov function control strategy proposed is confirmed.