A curved display device and a curved display panel are provided. The curved display panel has a first side surface and a second side surface opposite to each other, and includes a first edge, a second edge, a third edge, and a fourth edge sequentially connected end to end. The first side surface is a smooth display surface. The first edge is opposite to the third edge, the second edge is opposite to the fourth edge, the first edge and the third edge are oppositely bent towards the first side surface, and the second edge and the fourth edge are oppositely bent towards the first side surface. The first edge, the second edge, the third edge, and the fourth edge of the curved display panel sequentially intersect at four corner points, and circle center points of curvature circles corresponding to the four corner points are located at a same point.