Classical Artificial Neural Networks (ANNs) though well exploited in solving classification problems, do not model perfectly the information encoding process in the human brain because ANNs encode information using rate-based coding. However, biological neurons in the brain are known to encode information using temporal coding. In order to mimic the biological method of encoding information, various Spiking Neural Network (SNN) models have been developed. However, some of these models are limited in the number of spikes and do not leverage well on some classification problems. In order to address some of the inherent challenges associated with SNN, a multi-layer learning model for a multi-spiking network is proposed in this paper. The model exploits the temporal coding of spikes and the least-squares method to derive a weight update scheme. It also employs a spike locality concept in order to determine how the synaptic weights are to be adjusted at a particular spike time so as to minimize the learning interference, and thereby, increasing the number of spikes for learning. The performance of the model is evaluated on benchmarked classification datasets. A correlation-based metric is combined with a threshold concept to measure the classification accuracy of the model. The experimental results showed that the proposed model achieved better classification accuracy than some state-of-the-art multi-layer SNN learning models. INDEX TERMS Multi-spiking neural network, supervised learning, temporal coding.