A high-pressure fuel pump for an internal combustion engine with direct injection of fuel into at least one combustion chamber of the internal combustion engine is provided. The high-pressure fuel pump includes a low-pressure connection for low-pressure fuel, wherein the low-pressure connection supplies low-pressure fuel to the high-pressure fuel pump, a low-pressure fuel supply chamber, a pump element and a high-pressure connection for discharging fuel from the high-pressure fuel pump. The low-pressure connection, the low-pressure fuel supply chamber, the pump element, and the high-pressure connection are provided in succession in a flow direction of the fuel. A medium-pressure fuel connection opens into a medium-pressure fuel supply chamber for supplying medium-pressure fuel to the high-pressure fuel pump. A fuel switching valve selectively connects the low-pressure fuel supply chamber or the medium-pressure fuel supply chamber in a fluid-conducting manner to the pump element.