This paper presents a novel framework, MGNER, for Multi-Grained Named Entity Recognition where multiple entities or entity mentions in a sentence could be non-overlapping or totally nested. Different from traditional approaches regarding NER as a sequential labeling task and annotate entities consecutively, MGNER detects and recognizes entities on multiple granularities: it is able to recognize named entities without explicitly assuming non-overlapping or totally nested structures. MGNER consists of a Detector that examines all possible word segments and a Classifier that categorizes entities. In addition, contextual information and a self-attention mechanism are utilized throughout the framework to improve the NER performance. Experimental results show that MGNER outperforms current state-of-the-art baselines up to 4.4% in terms of the F1 score among nested/non-overlapping NER tasks.