Ship meteorological path planning has received increasing attention, especially in the dynamic wind, wave, and current environments. Determining a safe and efficient voyage path is one of the most important issues for ships. In order to reduce the navigation costs in terms of distance, energy, and time under multiple constraints, a novel ship path planning method is proposed in a spatially-temporally variant environment, which can find the optimum paths under different task requirements. An improved A* algorithm in a dynamic current environment (A*-DCE) is proposed, which introduces the weights of distance, energy, and time to generate paths with significantly different costs. The attractive/repulsive field replaces the distance cost estimation of the conventional A* algorithm. The grid map is segmented based on velocity data to determine energy and time cost estimations. Under the varied spatial-temporal current environment in the Nw-European Shelf region, the B-spline curve is used to improve the smoothness and to reduce the yaw cost. In addition, the paths in the candidate set that conform to the Pareto front are obtained using the NSGA-II algorithm. The smallest distance path has the same distance-optimal capability as the path from the conventional A* algorithm. The energy and time cost of the remaining optimal paths are also reduced.