The invention discloses a pneumatic expansion core clamping device of a lathe. The clamping device comprises a clamping mechanism, a fixing base, a cylinder fixing base and a drive mechanism, the clamping mechanism, the fixing base, the cylinder fixing base and the drive mechanism are sequentially arranged in the horizontal direction, the fixing base is of a horizontal hollow structure, a rotating transmission mechanism is hidden in the fixing base and penetrates through the cylinder fixing base, the clamping mechanism and the drive mechanism are fixedly connected through the rotating transmission mechanism, the rotating transmission mechanism is pulled by the drive device under linkage action, and then the clamping mechanism is driven to clamp and loosen a workpiece. The invention further provides an operation method of the pneumatic expansion core clamping device of the lathe. According to the designed clamping device and the operation method, clamping is achieved by means of a pneumatic expansion core clamping mode instead of a bolt manual screwing mode, the structure is simple, operations are convenient to carry out, cost is low, labor intensity is reduced, the assembling and clamping processes are stable and controllable, assembling and clamping time of lathe machining is greatly shortened, and production efficiency of the lathe is improved.