The present invention relates to a cover apparatus for a truck cargo box, and more specifically to a cover apparatus for a truck cargo box, which enables stable opening and closing operations even when deformation occurs due to the deflection or warping of a truck cargo box and enables its covers to stably cover irregularly shaped loads, such as various types of wastes or scraps, thereby considerably improving transportation safety and the convenience of use. According to the present invention, there is provided the cover apparatus for a truck cargo box, which enables stable opening and closing operations via the hinges and the variable members, and enables its covers to stably cover irregularly shaped loads via the covers in each of which the plurality of blocks is connected to each other, thereby providing the effect of considerably improving transportation safety and the convenience of use.