An important issue in the PC grid computing environment that is characterized by volatility and heterogeneity is the minimization of execution time for all tasks. This paper proposes a scheduling mechanism to reduce such execution time by means of both checkpoint sharing and task duplication under a peer-to-peer (P2P) architecture. In the mechanism, the checkpoint executed by an individual peer (i.e., a desktop PC) is used as an intermediate result and executed in other peers via its duplication and transmission. As a result, as the checkpoint is close to a final result, the reduction of execution time for each task becomes higher. Ultimately, turnaround time can be reduced. Moreover, an analytical model with an embedded Markov chain is presented to evaluate the transmission cost and execution time of our scheduling mechanism. The performance of our scheduling mechanism is also compared with that of the existing mechanism operating on client-server architecture. The analytical results show that our scheduling mechanism is superior to the existing mechanism with respect to the reduction of execution time.