Real-time disk scheduling is an important research topic for time-critical multimedia applications. Some well-known research results, such as SCAN-earliest deadline first (EDF) and DM-SCAN, applied the SCAN scheme to reschedule service sequence of input tasks and reduce their service time. In this paper, we prove that the general disk-scheduling problem with linear cost-function is NP-Hard. We also propose the shortest-task-first-DM, a new real-time disk-scheduling algorithm using the concept of the shortest-task-first and the deadline modification. As shown in the experimental results, our approach can schedule more tasks to meet their deadlines.