Recently, the problem of scheduling readers to read maximum tags such that readers and tags can be avoided collision within a given multiple interrogation ranges of reader has received a great deal of attention in Radio frequency identification (RFID) systems. Many methods have been proposed for the RFID systems such that readers can read maximum tags. However, most of previous works often require lots of readers or exist reader-tag collisions. In this paper, we propose a new algorithm, called the Dynamic-Range-based algorithm (DRBA), to maximize the number of read tags and avoid collisions within the multiple interrogation ranges of readers. Simulation results show that the DRBA has better performance than other existing methods.