A fuel supply device for a liquefied petroleum direct injection (LPDI) engine in which liquefied petroleum gas (LPG) is directly injected into a combustion chamber and a start control method of an LPDI engine having the fuel supply device, wherein the high pressure fuel pump receives and compresses fuel to a pressure higher than a pressure at which fuel has been supplied, wherein the high pressure fuel rail buffers and supplies fuel to a direct injector that injects fuel directly into a combustion chamber, wherein the return line is connected to the supply line through the high pressure fuel pump to form a low pressure line, allowing a surplus portion of fuel supplied to the high pressure fuel pump from the fuel tank to return to the fuel tank, and wherein a first valve is disposed on the return line to control the flow rate of returning fuel.