Summary: This paper proposes a spiking neural network (SNN) of the mammalian auditory midbrain to achieve binaural multiple sound source localisation. The network is inspired by neurophysiological studies on the organisation of binaural processing in the medial superior olive (MSO), lateral superior olive (LSO) and the inferior colliculus (IC) to achieve a sharp azimuthal localisation of sound sources over a wide frequency range in a reverberant environment. Three groups of artificial neurons are constructed to represent the neurons in the MSO, LSO and IC that are sensitive to interaural time difference (ITD), interaural level difference (ILD) and azimuth angle respectively. The ITD and ILD cues are combined in the IC to estimate the azimuth direction of a sound source. To deal with echo, we propose an inter-inhibited onset network in the IC, which can extract the azimuth information from the direct path sound and avoid the effects of reverberation. Experiments show that the proposed onset cell network can localise two sound sources efficiently taking into account the room reverberation.