Broadcast filtering technique is useful in reducing the snoopenergy consumption of shared bus-based MPSoCs by intelligently avoiding useless coherency-request broadcasts. Since the patterns of coherency-request broadcasts are highly dependent on how concurrent tasks are assigned to multiple processors, a broadcast filtering-aware task assignment is important in achieving a high-level of energy efficiency for MPSoCs with a broadcast filtering support. In this paper, we propose broadcast filtering-aware task assignment techniques for low-power MPSoCs, taking advantage of the patterns of coherency-request broadcasts of given tasks. We first propose a restricted optimal task assignment technique that can be useful only when the number of tasks is equal to the number of processors. Then, we describe a general task assignment heuristic that can be used for the arbitrary number of tasks.Experimental results show that when the number of tasks is equal to the number of processors, the proposed optimal task assignment technique reduces the snoop energy consumption by 13% over naive task assignment cases. For general task sets, the proposed task assignment heuristic reduces the snoop energy consumption by 15% over naive task assignment cases.