A method of operating a cryogenic fuel system for supplying fuel to an engine is provided herein. A cryogenic fuel pump is operated to pump fuel to be supplied to the engine. At least a portion of the pumped fuel is diverted to be supplied to an accumulator, when a fuel demand of the engine is less than a discharge output of the cryogenic fuel pump. Further, the supply of the pumped fuel from the cryogenic fuel pump to the engine and the accumulator is stopped, when a pressure within the accumulator reaches a first predefined pressure limit. Furthermore, the fuel is supplied to the engine from the accumulator, when supply of the pumped fuel from the cryogenic fuel pump to the engine and the accumulator is stopped.