This paper works on a new task - Tail Entity Recognition and Linking (TERL) for Knowledge Graphs (KG), i.e., recognizing ambiguous entity mentions from the tails of some relational triples, and linking these mentions to their corresponding KG entities. Although plenty of work has been done on both entity recognition and entity linking, the TERL problem in this specific scenario is untouched. In this paper, we work towards the TERL problem by fully leveraging KG information with two neural models for solving the two sub-problems, i.e., tail entity recognition and tail entity linking respectively. We finally solve the TERL problem end-to-end by proposing a joint learning mechanism with the two proposed neural models, which could further improve both tail entity recognition and linking results. To the best of our knowledge, this is the first effort working towards TERL for KG. Our empirical study conducted on real-world datasets shows that our models can effectively expand KG and improve the quality of KG.