In this paper, a speaker verification algorithm, which is inspired by the physiology of hearing in the human auditory system, is proposed. The algorithm uses a modified self‐organising map composed of spiking neurons. The architecture of the algorithm imitates the biomechanical mechanism of the human auditory system, which converts the speech signal from sound vibration waves into electrical spikes inside the cochlea. The paper also suggests a spike‐based rank order coding input feature vector, which is designed to be representative of the real biological spike trains found within the human auditory nerve. During the training phase, the winner neuron in the proposed Spiking Self‐Organising Map is updated only when its activity exceeds a specified threshold. The algorithm is evaluated using 50 speakers from the Centre for Spoken Language Understanding (CSLU2002) speaker verification database and shows a speaker verification performance of 90.1%. This compares favourably with previous non‐spiking self‐organising map that used Discrete Fourier Transform‐based input feature vector with the same dataset.