The invention relates to a gripper device of a flat plate support. The gripper device comprises a fixed gripper, a cover plate and a movable gripper. The fixed gripper comprises a body part and a circular protruding part. A plurality of gear blocks which are evenly distributed are arranged on the outer circumferential face of the circular protruding part. A gear clamping groove is formed in each gear block. The body part of the fixed gripper comprises a bottom wall, side walls and a rear wall, wherein a containing tank is formed by the bottom wall, the side walls and the rear wall in a defined manner. A plurality of spring installation grooves are formed in the bottom wall. Springs are installed in the spring installation grooves. A plurality of fixing columns are arranged above the bottom wall. The bottom wall is bent and extends to be provided with a fixed gripper part. The movable gripper comprises a base part and a movable gripper part bent and extending from the base part. Spring abutting parts matched with the springs are arranged on the base part. The base part is provided with a plurality of limiting grooves matched with the fixing columns. A lock catch device and an unlocking insertion piece are installed in the fixed gripper, and therefore the gripper device can be suitable for tablet personal computers of different sizes, and the tablet personal computers can be freely taken.