An insulation structure of a cargo tank in an LNG carrier and a method of constructing the insulation structure are disclosed. By providing an insulation structure of a cargo tank in an LNG carrier and a method of constructing the insulation structure, which includes a first metal foil attached and installed in between the top insulation panel and the bottom insulation panel, a second metal foil attached to and installed on the first metal foil that is positioned on an upper side of a gap formed between the bottom insulation panels, and a top bridge panel attached to and installed on an upper side of the second metal foil, the sealing integrity of the cargo tank can be improved.