State-of-the-art Named Entity Recognition (NER) models rely heavily on large amounts of fully annotated training data. However, accessible data are often incompletely annotated since the annotators usually lack comprehensive knowledge in the target domain. Normally the unannotated tokens are regarded as non-entities by default, while we underline that these tokens could either be non-entities or part of any entity. Here, we study NER modeling with incomplete annotated data where only a fraction of the named entities are labeled, and the unlabeled tokens are equivalently multi-labeled by every possible label. Taking multi-labeled tokens into account, the numerous possible paths can distract the training model from the gold path (ground truth label sequence), and thus hinders the learning ability. In this paper, we propose AdaK-NER, named the adaptive top-K approach, to help the model focus on a smaller feasible region where the gold path is more likely to be located. We demonstrate the superiority of our approach through extensive experiments on both English and Chinese datasets, averagely improving 2% in F-score on the CoNLL-2003 and over 10% on two Chinese datasets compared with the prior state-of-the-art works.