Due to the more stringent regulations on pollutant and greenhouse gas emissions in the maritime transport sector, solutions are being sought to reduce or avoid the emissions generated during the operation of ships. The onboard installation of hydrogen-fuelled fuel cells is a solution respectful with the environment and the marine ecosystem through which ships navigate. In this work, the design of a wellboat and its power plant based on fuel cells fed with hydrogen and hybridised with batteries is conducted, making it a zero-emissions ship that can navigate Emission Control Areas (ECAs). The fuel cells used are polymer electrolyte membrane fuel cells (PEMFCs), and the hydrogen they consume is stored in tanks pressurised at 35 MPa, grouping these tanks into three standard containers (Twenty-Foot Equivalent Units) installed on an exposed deck. The electrical and propulsion needs of the ship are covered by the installed power plant, providing an average power of 1266 kW and a peak power of 2624 kW, making it possible to avoid the emission of 10.8 t of CO2, 195 kg of NOx and 9 kg of SOx per 14 h mission.