The moldable parallel task (MPT) is a kind of parallel task that their sub-tasks hold the resources exclusively, which has been widely used in different areas. Our paper focuses on the scheduling of moldable tasks when every sub-task supports time-slice. The time-slice is a consecutive time that the sub-task holds the resources exclusively. After every time-slice, the sub-task can be canceled, suspended, or continued. We give the model of MPTs and propose a scheduling method for MPTs: MC (a heuristic scheduling method supporting time-slice model on the cloud). The simulation results show that, even under a forecast accuracy of system load under 90% and 95%, MC reduces average waiting time and average execution time; at the same time, MC has a lower value in the percentages of unfinished tasks. INDEX TERMS Moldable parallel task, speedup, parallelism, scheduling method.