A curved backboard assembly includes a curved metal plate and a curved plastic plate mounted to the curved metal plate. The curved metal plate includes longitudinal positioning slots and a set of transverse positioning slots, and the curved plastic plate includes longitudinal positioning pawls and a set of transverse positioning pawls. Each of the longitudinal positioning pawls is received into and set in engagement with one of the longitudinal positioning slots. The curved plastic plate is compressible to allow the transverse positioning pawls to be respectively received into and set in engagement with the transverse positioning slots and a spring force exerted by the curved plastic plate keeps the transverse positioning pawls in the transverse position slots. A curved display device that includes the above curved backboard assembly is also provided.