A flexible display device is provided. A first support member is fixed to a housing, a second support member is slidably arranged relative to the first support member; a flexible display screen is disposed on a side of the first support member and the second support member, the first end is connected to an end of the second support member, and the second end is connected to the transmission mechanism in the housing; and when the first support member slides relative to the second support member, the transmission mechanism keeps movements of both ends of the flexible display screen in a same movement distance at a same time.