System for supplying liquefied natural gas fuel

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 (20). In addition, the system senses LNG flowing to a glycol tank (61) of the heating circuit using a pressure sensor (65), etc. when the LNG flows to the glycol tank (61) due to pressure difference between a fuel supplying line (21) and a glycol circulation line (64) in the case when a the LNG/glycol water heat exchanger (50) is leaking, and outputs the leacked LNG to the outside via LNG removal line (67). As a result, the glycol circulation line (64) may be returned to original state and stability of the system may be enhanced.