System for supplying liquefied natural gas fuel

A system (1) for supplying fuel includes a fuel supplying line (21) connected from a fuel storage tank (10) to an engine (20) and including a pressure measuring sensor (23), a pump (30) provided on the fuel supplying line and configured to pressurize fuel outputted from the fuel storage tank (10), a heat exchanger (50) provided on the fuel supplying line (21) between the pump (30) and the engine (20) and configured to heat the fuel outputted from the pump (30), a first return line (11)provided at a front end of the heat exchanger on the fuel supplying line (21) and configured to return the fuel from the fuel supplying line (21), and a second return line (113) provided at a rear end of the heat exchanger (50) on the fuel supplying line (21) and configured to return the fuel from the fuel supplying line (21).