A flexible second gas barrier for a liquefied gas storage tank which includes a stiffener fabric weaved with two or more kinds of fiber yarn selected from a group consisting of a glass fiber, a carbon fiber, an aramid fiber, and a synthetic fiber. The stiffener fabric is weaved so that a hybrid fiber yarn is made by 2-ply yarning two or more kinds of a single yarn or a twisted yarn of fiber yarn selected from a group consisting of a glass fiber, a carbon fiber, an aramid fiber, or a synthetic fiber, is included in the weft and/or warf so that repeated fatigue resistance, even under cryogenic conditions, is achieved, which ultimately has the effect of solving the problems associated with repeated load increase imposed on the second gas barrier as the thickness of LNGC Foam increases.