The invention provides a translational gear-rack clamping device, and belongs to the technical field of clamps. The translational gear-rack clamping device comprises a rack, a gear, a flexible shaft and a pneumatic motor, wherein an upper folded plate support seat is arranged on an upper guide rail in a manner of sliding to left and right; a lower folded plate support seat is arranged on a lower guide rail in a manner of sliding to left and right; a guide rod is arranged on a guide rod support seat in a manner of sliding up and down; the lower end of a guide rod is inserted into a lower bearing sleeve of the guide rod, and slidably connected with the lower bearing sleeve of the guide rod; the upper end of the rack is fixed to an upper clamping jaw support seat; the lower end of the rack isinserted into a lower bearing sleeve of the rack, and slidably connected with the lower bearing sleeve of the rack; the gear and the rack are mutually engaged; a motor support seat is arranged on a concave seat in a manner of sliding to left and right; the pneumatic motor is installed on the motor support seat; the pneumatic motor is connected with a gear shaft through the flexible shaft; and a guide assembly and a stretching cylinder are arranged in a staggered manner. According to the translational gear-rack clamping device provided by the invention, the parallel movement of a clamping jawis realized through the gear and the rack, clamping and releasing for a workpiece are rapidly realized, and moreover, the gear is connected with the pneumatic motor through the flexible shaft, so thata compact structure is achieved.