A fuel pump for a liquid fuel water injection system of a motor vehicle is provided. The fuel pump includes a low-pressure pump that mixes water from a water tank of the motor vehicle with liquid fuel from a fuel tank of the motor vehicle to a liquid fuel water emulsion and provides the liquid fuel water emulsion at a low pressure. A high-pressure pump is in fluid communication with the low-pressure pump and compresses the liquid fuel water emulsion from the low pressure to a high pressure for injecting the liquid fuel water emulsion into an internal combustion engine of the motor vehicle via an injection rail of the motor vehicle. A pump drive drives the low-pressure pump and the high-pressure pump synchronously with a pump frequency independently from an engine speed of the internal combustion engine of the motor vehicle.