An apparatus disclosed relates to a technique for applying adhesive tape to a workpiece. The apparatus includes a chuck table for receiving and holding the workpiece, a tape feeding device for feeding adhesive tape in strip form toward the workpiece held by the chuck table, an applying device for placing an applicator roller in contact with a surface of the adhesive tape and applying the adhesive tape to a surface of the workpiece, and a vibration generating mechanism for vibrating the applicator roller.