A pulley assembly connecting an ISG driveshaft of an ISG and an engine to each other through a belt may include: a pulley member around which the belt is wound; a spring hub fixed to an internal peripheral surface of the pulley member; an ISG hub rotatably disposed when the ISG hub is distanced from an internal peripheral surface of the spring hub by a predetermined interval and connected to the ISG driveshaft; a limit device provided in the spring hub and ISG hub and limiting a rotation of the ISG hub to rotation by a predetermined rotation angle; and a plurality of leaf springs radially inserted into the spring hub in a circumferential direction thereof, and having one end portions fixed to the spring hub and the other end portions penetrating the ISG hub.