A compensator drive device comprises a drive head (10), a transmission shaft (20), a drive wheel (30), and a mounting base (40). The drive wheel (30) is provided within a first placement cavity (41) of the mounting base (40) and rotates along its own axis. One end of the transmission shaft (20) is connected to the drive wheel (30), and the other end of the transmission shaft (20) is protruded from a first end of the mounting base (40) and is connected to one end of the drive head (10). When driving a compensating box steel tube, the other end of the drive head (10) is embedded into an end of the compensating box steel tube of the compensator, and the drive head (10) and the transmission shaft (20) are rotated under the driving of the drive wheel (30), so as to drive the compensating box steel tube to rotate. The first end of the mounting base (40) is provided with a gland (50), a first through-hole (51) for the transmission shaft (20) penetrating through is provided on the gland (50), and the inner diameter of the first through-hole (51) is decreased gradually from the side close to the drive head (10) to the side close to the mounting base (40). Meanwhile, a compensator comprising the drive device is provided. The drive device has a long lifetime and low maintenance cost.