The system heats glycol water using steam generated by a boiler and heating LNG using the glycol water, thereby increasing efficiently the LNG to temperature required for an engine. In addition, the system senses LNG flowing to a glycol tank using a pressure sensor, etc. when the LNG flows to the glycol tank due to pressure difference between a fuel supplying line and a glycol circulation line generated according as a heat exchanger is broken down, and outputs the flowed LNG to the outside. As a result, the glycol circulation line may be returned to original state and stability of the system may be enhanced.