In this paper, a spiking neural network (SNN) architecture to simulate the sound localization ability of the mammalian auditory pathways using the interaural intensity difference cue is presented. The lateral superior olive was the inspiration for the architecture, which required the integration of an auditory periphery (cochlea) model and a model of the medial nucleus of the trapezoid body. The SNN uses leaky integrate-and-fire excitatory and inhibitory spiking neurons, facilitating synapses and receptive fields. Experimentally derived head-related transfer function (HRTF) acoustical data from adult domestic cats were employed to train and validate the localization ability of the architecture, training used the supervised learning algorithm called the remote supervision method to determine the azimuthal angles. The experimental results demonstrate that the architecture performs best when it is localizing high-frequency sound data in agreement with the biology, and also shows a high degree of robustness when the HRTF acoustical data is corrupted by noise.