Asymmetry of in/out-degree distribution is a widespread phenomenon in real-world complex networks. This paper put forward the concept of Edge Asymmetry(EA) to quantify this feature. We designed an EA-based strategy to attack six kinds of real-world networks and found that it was able to achieve the effect as well as edge betweenness-based(EB) and better than edge degree-based(ED) and random attack strategies. In simulation, we found that the greater the network asymmetry the better the EA-based attack strategy performed. By definition, the computational complexity of EA was much lower than that of EB. Therefore, EA-based attack strategies were superior in efficiency. We verified the effect of the EA-based attack strategy with four groups of large-scale networks.