Link prediction is a challenging problem for complex network analysis, arising in many disciplines such as social networks and telecommunication networks. Currently, many existing approaches estimate the proximity of the link endpoints for link prediction from their feature or the local neighborhood around them, which suffer from the localized view of network connections and insufficiency of discriminative feature representation. In this paper, we consider the problem of link prediction from the viewpoint of learning discriminative path-based proximity ranking metric embedding. We propose a novel ranking metric network learning framework by jointly exploiting both node-level and path-level attentional proximity of the endpoints for link prediction. We then develop the path-based dual-level reasoning attentional learning method with recurrent neural network for proximity ranking metric embedding. The extensive experiments on two large-scale datasets show that our method achieves better performance than other state-of-the-art solutions to the problem.