This paper presents a supervised learning algorithm, namely, the Synaptic Efficacy Function with Meta-neuron based learning algorithm (SEF-M) for a spiking neural network with a time-varying weight model. For a given pattern, SEF-M uses the learning algorithm derived from meta-neuron based learning algorithm to determine the change in weights corresponding to each presynaptic spike times. The changes in weights modulate the amplitude of a Gaussian function centred at the same presynaptic spike times. The sum of amplitude modulated Gaussian functions represents the synaptic efficacy functions (or time-varying weight models). The performance of SEF-M is evaluated against state-of-the-art spiking neural network learning algorithms on 10 benchmark datasets from UCI machine learning repository. Performance studies show superior generalization ability of SEF-M. An ablation study on time-varying weight model is conducted using JAFFE dataset. The results of the ablation study indicate that using a time-varying weight model instead of single weight model improves the classification accuracy by 14%. Thus, it can be inferred that a single input-output layer spiking neural network with time-varying weight model is computationally more efficient than a multi-layer spiking neural network with long-term or short-term weight model.