In this paper, we study a novel approach for named entity recognition (NER) and mention detection in natural language processing. Instead of treating NER as a sequence labelling problem, we propose a new local detection approach, which rely on the recent fixed-size ordinally forgetting encoding (FOFE) method to fully encode each sentence fragment and its left/right contexts into a fixed-size representation. Afterwards, a simple feedforward neural network is used to reject or predict entity label for each individual fragment. The proposed method has been evaluated in several popular NER and mention detection tasks, including the CoNLL 2003 NER task and TAC-KBP2015 and TAC-KBP2016 Tri-lingual Entity Discovery and Linking (EDL) tasks. Our methods have yielded pretty strong performance in all of these examined tasks. This local detection approach has shown many advantages over the traditional sequence labelling methods.