The present invention provides a torque transmission device for a compressor, which prevents parts constituting the torque transmission device from disengaging when a torque limiter is engaged, minimizes the occurrence of foreign matter entry through elongated holes between breakage portions prior to torque limiter engagement and also through a gap formed at the breakage portions after the torque limiter engagement and reduces the occurrence of noise at the time of torque limiter engagement. The torque transmission device comprises a pulley 2, a hub unit 3, a first disk unit 4 and a second disk unit 5. Breakage portions 20, over which breakage occurs when the transmission torque received at the pulley 2 becomes equal to or greater than a predetermined level, are formed at the first disk unit 4. The breakage portions 20 are set in relative proximity to a drive shaft 12. The end of the second disk unit 20 toward the drive shaft is set closer to the drive shaft 12 than the breakage portions 20, and the second disk unit 5 includes recessed portions 13 ranging from an area around a pass whole 9 at which the hub unit 3 is inserted toward an area of the second disk unit that faces opposite the breakage portions 20.