Maritime transport accounts for 80-90% of international trade and is crucial to the world economy. This industry released more than 1 billion tonnes of carbon dioxide (CO2) each year, accounting for 2-3% of global anthropogenic CO2 emissions. International organizations and government agencies, such as International Maritime Organization and European Union, have established strict rules to drastically reduce CO2 emissions from maritime transport. Onboard carbon capture is a promising solution for the maritime transport industry to reduce its CO2 emissions and meet its decarbonization goals. In this paper, we present a feasibility study and a conceptual design for an onboard carbon capture and storage system based on a new generation of polymeric CO₂-removal membranes. Using the ASPEN® and MATLAB® simulation software, we have verified that this system can achieve a gross carbon capture efficiency of more than 95% and store the captured CO2 onboard as liquid CO2. In addition, we have compared the developed system with two decarbonization approaches: (1) using biofuels with low carbon density instead of using traditional petroleum-based fuels such as heavy fuel oil, and (2) using onboard amine scrubbing for carbon capture, under various gross carbon capture efficiencies and different ship engine loads. A life cycle analysis was also conducted to compare these three decarbonization approaches.