A fixing device of a first barrier-reinforcing member for supporting first and second corrugated portions that are formed in a first barrier to cross each other in a liquefied natural gas (LNG) storage tank including a heat-insulating board and a first barrier positioned thereon and forming an inner wall, includes: a fixing bracket including a coupling portion fixedly inserted in insertion grooves formed under lateral sides of a crossing portion where the first and second corrugated portions cross, and a body coupled to one side of the coupling portion; and a first fastening member for fastening an impact-absorbing plate between the heat-insulating board and the first barrier with the other side of the body. The reinforcing member is fixed to inner sides of the first and second corrugated portions by the impact-absorbing plate.