Disclosed is a CD player that ensures a setup operation and reproduction of information even when a partially recorded CD-R is set therein. The CD player sequentially performs the setup operation, starting from the first setup position located at the innermost periphery of the CD, predetermined for the setup operation, until the setup operation is complete at any of n-th (n=2, 3, . . . ) setup positions lying outwardly of the first setup position. If the setup operation is not completed even at an n-th setup position located at the outermost periphery of the CD, the CD player performs the setup operation again at at least one setup position lying inwardly of the n-th setup position. Also disclosed is a CD player that can discriminate a partially recorded, additionally recordable CD-R, and can execute the reproduction control for the PRD. This CD player discriminates a set disk as an additionally recordable one when a mirror-finished portion is detected in the control to detect the lead-in area or when the lead-in area cannot be detected and the TOC information cannot be read.