A genetic algorithm (GA) has been employed to optimize the major design variables of the liquid rocket engine. Pressure of the main combustion chamber, nozzle expansion ratio and O/F ratio have been selected as design variables. The target engine has the open gas generator cycle using the LO2/RP-1 propellant. The gas properties of the combustion chamber have been obtained from CEA2 and the mass has been estimated using reference data. The objective function has been set as multi-objective function with the specific impulse and thrust to weight ratio using the weight method. The result shows about 4% improvement of the specific impulse and 23% increase of the thrust to weight ratio. The Pareto frontier line has been also obtained for various thrust requirements.