Spiking Neural Networks (SNNs) are regarded as the third generation of neural network models, which can learn the precise spike trains of the stimuli. As speech signals exhibit strong temporal structure, SNNs are a natural choice for learning temporal dynamics of the speech. Therefore, we propose a unified biologically plausible framework using spiking neurons with temporal coding and supervised learning to solve the auditory attention problem. We further introduce momentum and Nesterov's accelerated gradient into the Remote Supervised Method to improve the performance and speed up the spike train learning. We evaluate our model on Grid corpus and demonstrate that our model performs a precise spike train coding for auditory attention and outperforms the baseline artificial neural networks.