This paper has considered the problem of preemptively scheduling a set of independent periodic hard real-time tasks in primary-backup based multiprocessor systems. An efficient scheduling algorithm—Task Partition based Fault Tolerant Rate-Monotonic (TPFTRM) is proposed which extends RM algorithm to primary-backup based multiprocessor to provide fault tolerance. Compared with previous scheduling algorithms in this area, TPFTRM abandons active backup copies and only uses passive and overlapping backup copies to maximize the backup over-booking and deallocation, thus improves the scheduling performance. Moreover, TPFTRM proposes the task partitioning and processors grouping technique, which reduce the scheduling computation time and also make an easy way to understand and implement it. Extensive simulations experiments are also carried out based on task sets with different parameters. And the simulation result shows a remarkable saving of processors as well as scheduling computation time compared with previous algorithms, which proves the feasibility and effectiveness of the oposed TPFTRM algorithm.