The trend of internal combustion engines is reducing or eliminating carbon emissions and improve the overall efficiency. The Argon Power Cycle hydrogen-fueled engine can specifically improve the thermal efficiency by employing argon as the working substance. At the same time, due to the utilization of hydrogen and oxygen, the combustion of the fuel in Argon Power Cycle hydrogen-fueled engines produces zero carbon emissions or NOx emissions. However, during engine operation, lubricating oil consumption can still generate CO2 and becomes the only source for carbon emissions. Furthermore, the accumulation of CO2 under closed cycle will impede the condensation recovery of argon and reduce the efficiency and power. In this study, a closed cycle model of Argon Power Cycle hydrogen-fueled engine was constructed, in which argon is recycled by condensation instead of being charged like air in an open cycle model. Effects of lubricating oil consumption and operation duration on CO2 accumulation, temperature and pressure at each engine process, combustion characteristics, net indicated thermal efficiency, and net indicated mean effective pressure were numerically investigated. The results show that the molar ratio of CO2 in the intake gas (CO2 fraction) grows with the increase of both lubricating oil consumption and operation duration, resulting in higher pressures during exhaust and intake processes. In addition, the peak combustion temperature (Tmax) decreases and thus the percentage of heat transfer loss decreases. However, the larger increment in the percentage of exhaust loss results in lower net indicated thermal efficiency and thus lower net indicated mean effective pressure. For 50 minutes of operation at lubricating oil consumption = 1.5 g/h, the CO2 fraction reaches 9.9%, with net indicated thermal efficiency decreasing from 53.7% to 50.4% and net indicated mean effective pressure decreasing from 0.53 MPa to 0.50 MPa. As a contrast, at lubricating oil consumption = 0.15 g/h, the CO2 fraction is 1.1%, with net indicated thermal efficiency = 53.4% and net indicated mean effective pressure = 0.52 MPa. Therefore, when the lubricating oil consumption is reduced to 0.15 g/h or carbon-free lubricating oil is used, the effect of lubricating oil consumption on Argon Power Cycle engine’s operation duration and efficiency will be effectively reduced or eliminated. This work will provide a reference for the development of the closed system of Argon Power Cycle such as lubricating oil consumption control strategy and CO2 capture device design.