A preemptive scheduling problem P|ptmn(δ)|C_max is proposed in this paper, in which an additional time cost δ is needed if a job is interrupted once. The problem has wide applications such as job allocation in projects, distributed computing and communication in networks. It is proved that P|ptmn(δ)|C_max is an NP-hard problem. An off-line approximation algorithm LPT-Wrap with time complexity of O(nlogn+m) and a performance ratio no more than 1.408 25 is presented. The on-line property ofP|ptmn(δ)|C_max is also studied and an on-line algorithm with linearitu time complexity and a competitive ratio of 2 is proposed.