One method by which the mammalian sound localization pathway localizes sound sources is by analyzing the microsecond-level difference between the arrival times of a sound at the two ears. However, how the neural circuits in the auditory brainstem precisely integrate signals from the two ears, and what the underlying mechanisms are, remains to be understood. Recent studies have reported that variations of axon myelination in the auditory brainstem produces various axonal conduction velocities and sophisticated temporal dynamics, which have not been well characterized in most existing models of sound localization circuits. Here, we present a spiking neural network model of the auditory brainstem to investigate how axon myelinations affect the precision of sound localization. Sound waves with different interaural time differences (ITDs) are encoded and used as stimuli, and the axon properties in the network are adjusted, and the corresponding axonal conduction delays are computed with a multi-compartment axon model. Through the simulation, the sensitivity of ITD perception varies with the myelin thickness of axons in the contralateral input pathways to the medial superior olive (MSO). The ITD perception becomes more precise when the contralateral inhibitory input propagates faster than the contralateral excitatory input. These results indicate that axon myelination and contralateral spike timing influence spatial hearing perception.