In a typical image captioning pipeline, a Convolutional Neural Network (CNN) is used as the image encoder and Long Short-Term Memory (LSTM) as the language decoder. LSTM with attention mechanism has shown remarkable performance on sequential data including image captioning. LSTM can retain long-range dependency of sequential data. However, it is hard to parallelize the computations of LSTM because of its inherent sequential characteristics. In order to address this issue, recent works have shown benefits in using self-attention, which is highly parallelizable without requiring any temporal dependencies. However, existing techniques apply attention only in one direction to compute the context of the words. We propose an attention mechanism called Bi-directional Self-Attention (Bi-SAN) for image captioning. It computes attention both in forward and backward directions. It achieves high performance comparable to state-of-the-art methods.