Utilizing CO2 capture and storage (CCS) technologies is a significant way to reduce carbon emissions from coal fired power plants. Cryogenic CO2 capture (CCC) is an innovative and promising CO2 capture technology, which has an apparent energy and environmental advantage compared to alternatives. A process of capturing CO2 from the flue gas of a coal-fired electrical power plant by cryogenically desublimating CO2 has been discussed and demonstrated theoretically. However, pressurizing the inlet flue gas to reduce the energy penalty for the cryogenic process will lead to a more complex system. In this paper, a modified CCC system utilizing a reverse Brayton Cycle is proposed, and the energy penalty of these two systems are compared theoretically.