In this paper, we describe a spiking neural network for building an azimuthal sound localization system, which is inspired by the functional organization of the human auditory midbrain up to the inferior colliculus (IC). Our system models two ascending pathways from the cochlear nucleus to the IC: an ITD (Interaural Time Difference) pathway and an ILD (Interaural Level Difference) pathway. We take account of Yin's finding [1] that multiple delay lines only exist in the contralateral medial superior olive (MSO) in our modeling of the ITD pathway. A level-locking auditory neuron is introduced for the ILD pathway network to encode sound amplitude into spike sequences. At the IC level, we differentiate between a low frequency (below 1 kHz) and high frequency (above 1 kHz) sound when combining the ITD and ILD cues to compute the azimuth angle of a sound. This paper provides a detailed illustration of the biological evidence of our hybrid ITD and ILD model. Experimental results of several types of sound are presented to evaluate our system. (This paper is an extension to one [2] of our papers in 2008 International Conference on Artificial Neural Networks.)