Provided is a method for operating a fuel supply system for a marine structure. The fuel supply system includes a BOG compression unit configured to receive and compress BOG generated in a storage tank, a reliquefaction apparatus configured to receive and liquefy the BOG compressed by the BOG compression unit, a high-pressure pump configured to compress the liquefied BOG generated by the reliquefaction apparatus, and a high-pressure gasifier configured to gasify the liquefied BOG compressed by the high-pressure pump. The fuel supply system includes a recondenser installed at an upstream side of the high-pressure pump, and the recondenser recondenses a portion or all of the generated BOG by using liquefied gas supplied from the storage tank. During a ballast voyage process, all of the BOG is supplied to and recondensed by the recondenser, and an operation of the reliquefaction apparatus is interrupted.