The ship weather routing has been a focus of nautical navigation research, many scholars have been committed to this research. This paper presented a general approach to determine the minimum voyage time route for the ship weather routing. The mathematical model of this method is based on the grid system, combined with genetic algorithms to determine a safe and time-saving route for ships. Based on the basic genetic algorithm, this paper introduced the deletion and insertion operator, and modified the mutation operator to make it more suitable for routing planning. The disadvantage of the optimized route obtained by the grid system is not smooth, therefore this paper introduced the smoothing operator to solve this problem. By sampling the waypoints of the optimized route to obtain its critical waypoints, the shape preserving piecewise cubic Hermite interpolation of the critical waypoint is carried out to obtain a smoother route. Simulation experiments of minimum voyage time routes on Norfolk and Lisbon had been conducted to demonstrate the capability of the algorithm within its framework.