A novel quality metric for binary edge maps, called the structural edge quality metric (SEQM), is proposed in this work. First, we define the matching cost between an edge pixel in a detected edge map and its candidate matching pixel in the ground-truth edge map. The matching cost includes a structural term, as well as a positional term, to measure the discrepancy between the local structures around the two pixels. Then, we determine the optimal matching pairs of pixels using the graph-cut optimization, in which a smoothness term is employed to take into account global edge structures in the matching. Finally, we sum up the matching costs of all edge pixels to determine the quality index of the detected edge map. Simulation results demonstrate that the proposed SEQM provides more faithful and reliable quality indices than conventional metrics.