The present invention provides a curvature-adjustable backboard assembly and a curved display device. The curvature-adjustable backboard assembly of the present invention includes a curvable backboard, a slider-crank mechanism, and a first low-speed position-limiting electric machine. The slider-crank mechanism comprises a central pivot and a first rail that are fixed to the backboard, a first slider mounted to the first rail, a first crank that is rotatable about the central pivot as being driven by the first low-speed position-limiting electric machine, and a first connection rod having two ends respectively and pivotally coupled to the first slider and the first crank, wherein when the first crank is driven to rotate, the first connection rod drives the first slider to move along the first rail and during the movement of the first slider along the first rail, a height of an arched form of the backboard with respect to the central pivot at a location where the first slider passes may vary accordingly so as to allow for easy and efficient variation of a curvature of the backboard according to a desired curving condition.