Parameter variations reveal themselves as different frequency and leakage powers per instances of the same MPSoC. By the increasing variation with technology scaling, worst-case-based scheduling algorithms result in either increasingly less optimal schedules or otherwise more lost yield. To address this problem, this paper introduces a variation-aware task and communication scheduling algorithm for multiprocessor system-on-chip (MPSoC). We consider both delay and leakage power variations during the process of finding the best schedule so that leakier processors are less utilized and can be more frequently put in sleep mode to reduce power. Our algorithm takes advantage of event tables to accelerate the statistical timing and power analysis. We use genetic algorithm to find the best schedule that maximizes power-yield under a performance-yield constraint. Experimental results on real world benchmarks show that our proposed algorithm achieves 16.6% power-yield improvement on average over deterministic worst-case-based scheduling.