In operating the underwater engines such as encountered in exploring submarines, the dumping of the exhaust gas out of the engine requires a large portion of the total power, frequently amounting to 25-30% of the power generated. This unfavorable circumstance can be cured by liquefying the exhaust gas and storing it. In the present study, two liquefaction systems were simulated to enhance the overall efficiency; one is a closed cycle diesel engine and the other is a closed cycle LNG engine. The liquefied natural gas (LNG) is chosen as a fuel, not only because its use is economical but also because its cold energy can be utilized within the liquefaction system. Since a mixture of oxygen and carbon dioxide is used as an oxidizer, liquefying carbon dioxide is of major concern in this study. For further improving this system, the intercooling of the compressor is devised. The necessary power consumed for the liquefying system is examined in terms of the related properties such as pressure and temperature of the carbon dioxide vessel as a function of the amount of the exhaust gas which enters the compressor. The present study was successful to show that much gain in the power and reduction of the vessel pressure could be achieved in the case of the closed cycle LNG engine. The compression power of exhaust gas were observed remarkably lower, typically only 6.3% for the closed cycle diesel engine and 3.4% for the closed cycle LNG engine respectively, out of net engine power. For practicality, a design -purpose map of the operating parameters of the liquefaction systems was also presented.