Binaural sound source localization (BSSL) in low signal-to-noise ratio (SNR) and high reverberation environment is still a challenging task. In this paper, a novel BSSL algorithm is proposed by introducing convolutional neural network (CNN). The proposed algorithm first extracts the spatial feature of each sub-band from binaural sound signal, and then combines the features of all sub-bands within one frame to assemble a two-dimensional feature matrix as a grey image. To fully exploit the advantage of the CNN in extracting high-level features from the grey image, the spatial feature matrix of each frame is used as input to train the CNN model. The CNN is then used to predict azimuth of sound source. The experiments show that the proposed algorithm significantly improves the localization performance of BSSL in various acoustic environments, especially to deal with low SNR and high reverberation conditions.