A stiffness reinforcement structure for a fuel tank of a vehicle includes: a reinforcing column having an upper opening and a lower opening, and side openings arranged at both sides of an upper end and both sides of a lower end thereof; sliders fastened to the side openings of the reinforcing column; an upper thermal bonding member inserted in the upper opening and fastened to corresponding sliders; a lower thermal bonding member inserted in the lower opening of the reinforcing column and fastened to corresponding sliders with a bottom thermally bonded to an inner side of the fuel tank; and springs wound around outer sides of the reinforcing column and the sliders and providing elastic compression force to the upper thermal bonding member and the lower thermal bonding member.