Most existing named entity recognition (NER) approaches are based on sequence labeling models, which focus on capturing the local context dependencies. However, the way of taking one sentence as input prevents the modeling of non-sequential global context, which is useful especially when local context information is limited or ambiguous. To this end, we propose a model called Global Context enhanced Document-level NER (GCDoc) to leverage global contextual information from two levels, i.e., both word and sentence. At word-level, a document graph is constructed to model a wider range of dependencies between words, then obtain an enriched contextual representation for each word via graph neural networks (GNN). To avoid the interference of noise information, we further propose two strategies. First we apply the epistemic uncertainty theory to find out tokens whose representations are less reliable, thereby helping prune the document graph. Then a selective auxiliary classifier is proposed to effectively learn the weight of edges in document graph and reduce the importance of noisy neighbour nodes. At sentence-level, for appropriately modeling wider context beyond single sentence, we employ a cross-sentence module which encodes adjacent sentences and fuses it with the current sentence representation via attention and gating mechanisms. Extensive experiments on two benchmark NER datasets (CoNLL 2003 and Ontonotes 5.0 English dataset) demonstrate the effectiveness of our proposed model. Our model reaches F1 score of 92.22 (93.40 with BERT) on CoNLL 2003 dataset and 88.32 (90.49 with BERT) on Ontonotes 5.0 dataset, achieving new state-of-the-art performance.