Deep spiking neural network (DSNN) is a promising computational model towards artificial intelligence. It benefits from both the DNNs and SNNs through a hierarchy structure to extract multiple levels of abstraction and the event-driven computational manner to provide ultra-low-power neuromorphic implementation, respectively. However, how to efficiently train the DSNNs remains an open question because of the non-differentiable spike function that prevents the traditional back-propagation (BP) learning algorithm directly applied to DSNNs. Here, inspired by the findings from the biological neural networks, we address the above-mentioned problem by introducing neural oscillation and spike-phase information to DSNNs. Specifically, we propose an Oscillation Postsynaptic Potential (Os-PSP) and phase-locking active function, and further put forward a new spiking neuron model, namely Resonate Spiking Neuron (RSN). Based on the RSN, we propose a Spike-Level-Dependent Back-Propagation (SLDBP) learning algorithm for DSNNs. Experimental results show that the proposed learning algorithm resolves the problems caused by the incompatibility between the BP learning algorithm and SNNs, and achieves state-of-the-art performance in single spike-based learning algorithms. This work investigates the contribution of introducing biologically inspired mechanisms, such as neural oscillation and spike-phase information to DSNNs and providing a new perspective to design future DSNNs.