A scheduling scheme is proposed to reduce execution time by means of both checkpoint sharing and task duplication under a peer-to-peer (P2P) architecture. In the scheme, the checkpoint executed by each peer (i.e., a resource) is used as an intermediate result and executed in other peers via its duplication and transmission. As the checkpoint is close to a final result, the reduction of execution time for each task becomes higher, leading to reducing turnaround time. To evaluate the performance of our scheduling scheme in terms of transmission cost and execution time, an analytical model with an embedded Markov chain is presented. We also conduct simulations with a failure rate of tasks and compare the performance of our scheduling scheme with that of the existing scheme based on client-server architecture. Performance results show that our scheduling scheme is superior to the existing scheme with respect to the reduction of execution time and turnaround time.