Nowadays deep learning is dominating the field of machine learning with state-of-the-art performance in various application areas. Recently, spiking neural networks (SNNs) have been attracting a great deal of attention, notably owning to their power efficiency, which can potentially allow us to implement a low-power deep learning engine suitable for real-time/mobile applications. However, implementing SNN-based deep learning remains challenging, especially gradient-based training of SNNs by error backpropagation. We cannot simply propagate errors through SNNs in conventional way because of the property of SNNs that process discrete data in the form of a series. Consequently, most of the previous studies employ a workaround technique, which first trains a conventional weighted-sum deep neural network and then maps the learning weights to the SNN under training, instead of training SNN parameters directly. In order to eliminate this workaround, recently proposed is a new class of SNN named deep spiking networks (DSNs), which can be trained directly (without a mapping from conventional deep networks) by error backpropagation with stochastic gradient descent. In this paper, we show that the initialization of the membrane potential on the backward path is an important step in DSN training, through diverse experiments performed under various conditions. Furthermore, we propose a simple and efficient method that can improve DSN training by controlling the initial membrane potential on the backward path. In our experiments, adopting the proposed approach allowed us to boost the performance of DSN training in terms of converging time and accuracy.