The invention relates to a marine fuel cell power supply system and a fuel cell ship. The marine fuel cell power supply system comprises a gas source, an air compressor, an air filter, a modular fuel cell assembly, a heat exchange device, a power distribution system and a control system, wherein the gas source arranged above a deck; the air compressor is arranged below the deck; the air filter is connected with an air inlet of the air compressor; the fuel gas input end of the modular fuel cell assembly is connected with the gas source, and the air input end of the modular fuel cell assembly is connected with an air outlet of the air compressor; the heat exchange device is arranged at the bottom of a cabin and is connected with a cooling pipe system in the modular fuel cell assembly; the power distribution system is connected with the power output end of the modular fuel cell assembly; and the control system is arranged in a control room and is connected with the power distribution system and the modular fuel cell assembly respectively. According to the invention, the power density is improved by adopting the modular design, the marine fuel cell power supply system can be applied to a relatively large ship, and integrated installation is not needed after the modular design is adopted, so that the installation of the ship fuel cell power supply system is more flexible, and the space in the ship can be better utilized for arrangement.