STDP is an unsupervised learning rule for synaptic plasticity which has been observed in different brain areas. STDP has been used in SNNs successfully, but in norm rate-based SNNs, the synaptic weight updates requires a large number of computations. In this paper, a time-based SNN with STDP is proposed. Only one neuron is selected to update its weights each time, therefore the synaptic weight updates cost is significantly reduced. The proposed network achieves 90.1% accuracy on MNIST dataset.