A fuel pump is obtained, by which a high fuel pump-up height and a short fuel pump-up time can be achieved without deteriorating a fuel injection state by discharging a vapor toward the [Means for Resolution] An air exhaust port having a channel area s satisfying s≧0.07 mm2 is provided in a lower channel including the terminal of a pump channel, and an air exhaust valve mechanism that opens the valve when the pump is started to exhaust intake air and closes the valve as soon as the application of pressure on the fuel is started to prevent the fuel from being exhausted to the outside of the pump channel is provided. Also, a vapor exhaust port is provided in the pump channel between the air exhaust port and the inlet portion of the pump channel, and a vapor exhaust valve mechanism that closes the valve when the pump is started to prevent a negative pressure at the fuel intake port from dropping and opens the valve when application of pressure on the fuel is started to exhaust fuel containing a vapor to the outside of the pump channel is provided.