In a magnetic disk apparatus using a composite thin-film magnetic head, high-speed reading and writing operations are achieved without increasing a read error rate and without decreasing a signal-to-noise ratio of read signals. The magnetic head is moved along an arc-like line on the magnetic disk having a track including a plurality of sectors. Each of the sectors has a data area and an identification area displaced from the data area due to movement of the magnetic head relative to the magnetic disk. A position identification sector which is positioned ahead of a target sector is determined based on a predetermined factor representing a period of time. An offset operation of the magnetic head is performed after the position identification sector is detected by a read head so that the magnetic head is moved from a first position to a second position. The read head tracks on the identification area when the head is at the first position and the read head tracks on the data area when the head is at the second position. The predetermined factor is measured since the identification sector was detected. A data reading operation is performed when a measured value of the predetermined factor reaches a predetermined value.