A roll-up tarp apparatus for a truck box having first and second ends, first and second longitudinal sides and an open top. The apparatus includes a tarp, a roll bar, an arm and a biasing member. The first longitudinal edge of the tarp is interconnected to the first longitudinal side of the truck box and the second longitudinal edge of the tarp is attached to the roll bar member. The roll bar is operatively connected to the truck box and is rotatably movable between the first and second longitudinal sides of the truck box, which enables the tarp to close or open the truck box. At least one biasing member is operatively connected to the roll bar or the arm, with the biasing member able to exert a tensioning force in the direction of the second longitudinal side of the truck box so that the tarp is under tension.