A display device and driving method for curved surface display are disclosed The display device includes a flat panel for achieving image display and a controllable liquid crystal cell above the flat panel for achieving curved surface display. The controllable liquid crystal cell includes an upper substrate and a lower substrate, and a liquid crystal layer between the upper substrate and the lower substrate. The lower substrate is an array substrate on which a plurality of driving electrodes for driving liquid crystals in the liquid crystal layer to deflect at different angles are provided. The display device further includes a signal controller for providing voltage signals for the driving electrodes, voltage signals for at least two driving electrodes being different.