Neural Network-based approaches have recently produced good performances in Natural language tasks, such as Supertagging. In the supertagging task, a Supertag (Lexical category) is assigned to each word in an input sequence. Combinatory Categorial Grammar Supertagging is a more challenging problem than various sequence-tagging problems, such as part-of-speech (POS) tagging and named entity recognition due to the large number of the lexical categories. Specifically, simple Recurrent Neural Network (RNN) has shown to significantly outperform the previous state-of-the-art feed-forward neural networks. On the other hand, it is well known that Recurrent Networks fail to learn long dependencies. In this paper, we introduce a new neural network architecture based on backward and Bidirectional Long Short-Term Memory (BLSTM) Networks that has the ability to memorize information for long dependencies and benefit from both past and future information. State-of-the-art methods focus on previous information, whereas BLSTM has access to information in both previous and future directions. Our main findings are that bidirectional networks outperform unidirectional ones, and Long Short-Term Memory (LSTM) networks are more precise and successful than both unidirectional and bidirectional standard RNNs. Experiment results reveal the effectiveness of our proposed method on both in-domain and out-of-domain datasets. Experiments show improvements about (1.2 per cent) over standard RNN.