In this study, optimization was performed to improve the conventional liquefaction process of offshore plants, such as a LNG-FPSO(Liquefied Natural Gas-Floating, Production, Storage, and Offloading unit) by maximizing the energy efficiency of the process. The major equipments of the liquefaction process are compressors, expanders, and heat exchangers. These are connected by stream which has some thermodynamic properties, such as the temperature, pressure, enthalpy or specific volume, and entropy. For this, a process design problem for the liquefaction process of offshore plants was mathematically formulated as an optimization problem. The minimization of the total energy requirement of the liquefaction process was used as an objective function. Governing equations and other equations derived from thermodynamic laws acted as constraints. To solve this problem, the sequential quadratic programming(SQP) method was used. To evaluate the proposed method in this study, it was applied to the natural gas liquefaction process of the LNG-FPSO. The result showed that the proposed method could present the improved liquefaction process minimizing the total energy requirement as compared to conventional process.