Named Entity Recognition (NER) is a fundamental problem in Natural Language Processing and has received much research attention. Although the current neural-based NER approaches have achieved the state-of-the-art performance, they still suffer from one or more of the following three problems in their architectures: (1) boundary tag sparsity, (2) lacking of global decoding information; and (3) boundary error propagation. In this paper, we propose a novel Boundary- aware Bidirectional Neural Networks (Ba-BNN) model to tackle these problems for neural-based NER. The proposed Ba- BNN model is constructed based on the structure of pointer networks for tackling the first problem on boundary tag sparsity. Moreover, we also use a boundary-aware binary classifier to capture the global decoding information as input to the decoders. In the Ba-BNN model, we propose to use two decoders to process the information in two different directions (i.e., from left-to-right and right-to-left). The final hidden states of the left-to-right decoder are obtained by incorporating the hidden states of the right-to-left decoder in the decoding process. In addition, a boundary retraining strategy is also proposed to help reduce boundary error propagation caused by the pointer networks in boundary detection and entity classification. We have conducted extensive experiments based on three NER benchmark datasets. The performance results have shown that the proposed Ba-BNN model has outperformed the current state-of-the-art models.