In this paper, we present our first Vietnamese speech synthesis system based on deep neural networks. To improve the training data collected from the Internet, a cleaning method is proposed. The experimental results indicate that by using deeper architectures we can achieve better performance for the TTS than using shallow architectures such as hidden Markov model. We also present the effect of using different amounts of data to train the TTS systems. In the VLSP TTS challenge 2018, our proposed DNN-based speech synthesis system won the first place in all three subjects including naturalness, intelligibility, and MOS.