A kind of Energy-efficient Scheduling Algorithm under the Constraint of Reliability (ESACR) for the random tasks in multiprocessor system was proposed. It would choose the processor which might consume the least energy when the task's deadline could be guaranteed. For the signal processor, Earliest Deadline First (EDF) strategy was used to schedule the tasks and all the tasks were made execute in the same voltage/frequency. When the new task could not match the deadline, the non-execution voltage/frequency of former tasks would be raised. At the same time, the recovery time was reserved for the executing task in order to promise that the task could be rescheduled when errors happened. The simulation shows that the ESACR can provide the better energy efficiency with the guarantee of system reliability , compared to Highest Voltage Energy-Aware (HVEA), Minimum Energy Minimum Completion time (ME-MC) and Earliest Finish First (EFF).