A device for regulating the pressure inside an on-board storage tank for cryogenic fuel such as natural gas, part of which is in the liquid state and another part of which is in the gaseous state, this cryogenic fuel being intended to supply a combustion chamber of an aircraft turbomachine, characterized in that it comprises: - an on-board tank for storing and supplying cryogenic fuel to said combustion chamber, this tank comprising a booster pump, located at the lower part of said on-board tank, - a mixing chamber, configured to be connected to said combustion chamber, - a first line connecting said on-board tank to said mixing chamber in order to allow the latter to be supplied with cryogenic fuel in the liquid state, this first line being provided with at least one pressurizing pump and a first regulation valve (410, 411), - a second line connecting said on-board tank to said mixing chamber in order to allow the latter to be supplied with cryogenic fuel in the gaseous state, this second line being provided with at least one compressor and a first control valve, - a recirculation line connecting said booster pump to the upper part of the tank, this recirculation line being equipped with a second regulation valve (432, 411) as well as a first heat exchanger that allows the cryogenic fuel to pass from the liquid state to the gaseous state, - a pressure sensor detecting the pressure inside said on-board tank, - a central control unit receiving pressure data from said pressure sensor and controlling the total or partial opening or the closing of the different regulation valves (410, 411, 432) and of the first control valve and the starting or stopping of the pressurizing pump, the booster pump and the compressor, as a function of the value of a setpoint pressure inside said on-board tank. - an on-board tank for storing and supplying cryogenic fuel to said combustion chamber, this tank comprising a booster pump, located at the lower part of said on-board tank, - a mixing chamber, configured to be connected to said combustion chamber, - a first line connecting said on-board tank to said mixing chamber in order to allow the latter to be supplied with cryogenic fuel in the liquid state, this first line being provided with at least one pressurizing pump and a first regulation valve (410, 411), - a second line connecting said on-board tank to said mixing chamber in order to allow the latter to be supplied with cryogenic fuel in the gaseous state, this second line being provided with at least one compressor and a first control valve, - a recirculation line connecting said booster pump to the upper part of the tank, this recirculation line being equipped with a second regulation valve (432, 411) as well as a first heat exchanger that allows the cryogenic fuel to pass from the liquid state to the gaseous state, - a pressure sensor detecting the pressure inside said on-board tank, - a central control unit receiving pressure data from said pressure sensor and controlling the total or partial opening or the closing of the different regulation valves (410, 411, 432) and of the first control valve and the starting or stopping of the pressurizing pump, the booster pump and the compressor, as a function of the value of a setpoint pressure inside said on-board tank.