||The invention relates to a power transmission device :or a clutchless compressor. The power transmission device comprises a pulley rotatably installed in a front housing of a compressor, a hub disposed in one side of the pulley and having a hub body to be connected with a driving shaft of the compressor, md a connector connecting the pulley with the hub. A flange is formed in one side face of the pulley. The hub has a cover plate integrally formed in the outer peripheral face of the hub body. The connector includes a drive-side connection member detachably connected to one side of the pulley through a first coupling means, a driven-side connection member connected to the hub through a second coupling means, and a breaking member for connecting the drive-side connection member with the driven-side connection member so as to be broken when a torque above a pre- 3et value is generated in the compressor.