To easily and surely draw off a fuel in a fuel pipe while an outboard motor is tilted up.

There is provided a fuel supply device 1 of an outboard motor 2 which supplies a fuel stored in a fuel tank into an intake port of an engine 13, and includes: a vapor separator 31 which separates a fuel sent from the fuel tank by a low-pressure fuel pump 30 into gas and liquid to release fuel vapor into the atmosphere; a fuel cooler 32 which is arranged below the vapor separator 31 to cool the fuel with cooling water passing through a cooling water pipe 51; a drain pipe 45 connected to a side surface 32a of the fuel cooler 32 which faces downward while the outboard motor is tilted up; and an in-line high-pressure fuel pump 33 connected to the middle of a fuel pipe 37e to be connected to a side surface of the fuel cooler 32 different from the side surface to which the drain pipe 45 is connected.