An liquefied natural gas (LNG) FPSO is a floating, production, storage, and offloading facility with a LNG plant, including all ancillary facilities. In contrast to commercial vessels, the various parts of the process are located topside and are distributed as modules that are installed on the deck. The design of an LNG FPSO requires many considerations such as international codes and standards, the owner's requirements, and the operation and maintenance philosophy. To resolve the many considerations in FPSO design, we proposed an optimization method for the topside arrangement in the previous study. Based on the previous study, an integrated optimization technique for an LNG FPSO is proposed to obtain the optimal principle dimensions, the arrangement of the hull tanks, and the layout of the topside modules and equipment that satisfies many requirements for not only the topside but also the hull. As a case study, the topside and hull layout of an LNG FPSO is optimized in terms of safety, economics, and stability. The case study shows that the proposed method can develop the optimal layout design of an LNG FPSO.