Although the precise symmetric forward and feedback connections between neurons are thought to be impossible in the brain, most existing deep spiking neural networks (SNNs) spatio-temporal learning algorithms still require such a strong architectural constraint to complete tasks. Besides that, as an expected feature for specialized neuromorphic hardware to be deployed, effective online learning of deep SNNs for training spatio-temporal data are still lacking. To address these issues, an effective biologically plausible asymmetric spatio-temporal online learning algorithm called ASTOL is proposed for training deep SNNs in real-time. ASTOL could learn the spatial and temporal features simultaneously in real-time, without the precise weights symmetric backpropagation and the need to know the duration of spatio-temporal data in advance. Experimental results show that the proposed ASTOL algorithm achieves comparable performance in real-time learning on the rate coding MNIST dataset and the temporal coding music MedleyDB dataset and speech TIDIGITS dataset with other state-of-the-art algorithms with simpler learning mechanism way as it avoids transport of synaptic weights. Besides that, the experiment on MNIST datasets also shows that ASTOL can use simpler network structures to achieve good performance faster.