We propose a biologically inspired binaural sound localization system using a deep convolutional neural network (CNN) for reverberant environments. It utilizes a binaural Cascade of Asymmetric Resonators with Fast-Acting Compression (CAR-FAC) cochlear system to analyze binaural signals, a lateral inhibition function to sharpen temporal information of cochlear channels, and instantaneous correlation function on the two cochlear channels to encode binaural cues. The generated 2-D instantaneous correlation matrix (correlogram) encodes both interaural phase difference (IPD) cues and spectral information in a unified framework. Additionally, a sound onset detector is exploited to generate the correlograms only during sound onsets to remove interference from echoes. The onset correlograms are analyzed using a deep CNN for regression to the azimuthal angle of the sound. The proposed system was evaluated using experimental data in a reverberant environment, and displayed a root mean square localization error (RMSE) of 3.68° in the -90° to 90° range.