Unlike the traditional omni-directional sensors that always have an omni-angle of sensing range, directional sensors may be able to switch to several directions and each direction has a limited angle of sensingrange. This paper studies a novel “area coverage by directional sensors” problem. It proposes the MaximumDirectional Area Coverage (MDAC) to maximize the covered area by scheduling the working directions of thesensors in the network. This paper proves the MDAC to be NP-complete and proposes two distributed schedulingalgorithms for the MDAC. The proposed algorithms are proved to terminate in finite time. Simulation results demonstrate the effectiveness of the two algorithms.