The present disclosure relates to an OLED display device and a method of packaging the OLED display device. An OLED display device, comprising: a substrate; a cover plate provided opposite to the substrate; a light emitting region located on a surface of the substrate facing the cover plate, wherein the light emitting region has an OLED display structure; a dam around the light emitting region; and a packaging adhesive layer disposed on the light emitting region and used to cover the OLED display structure, wherein the cover plate is provided with a groove at a position corresponding to the dam, an end of the dam away from the substrate being disposed in the groove.