A curved surface display device and a curved surface display method, which belong to the field of display technology. The curved display device comprises a display panel, a motor, a first arc lever and a second arc lever. A first end of the first arc lever and the second arc lever are connected with the motor through a connector, and a second end of the first arc lever and second arc lever are connected with the casing of the device. The connector is used for pulling the first end of the first arc lever and the first end of the second arc lever with rotation of the motor, such that the first arc lever and the second arc lever rotate around their pivots respectively, thus realizing automatic bending of the casing, which meets the user's requirement of adjusting the curvature of the curved surface display device.