Nesting and cutting path optimization have a great effect on the price competition and improvement of productivity in various industries such as shipbuilding, automobile, clothing, and so on. But the theoretical approach on the development of cutting path optimization algorithm, which can be applied effectively in the shipbuilding, has not been performed enough because structural parts of a ship are so complex and various. In this study, a new approach has been suggested to solve the cutting path problem in 2-D cutting by using genetic algorithm and cutting sequence of each part by its center of gravity. The presented optimization algorithm can search the cutting sequence of parts by applying the effective neighborhood solution generating method.