Deep neural networks (DNNs) have provably enhanced the state-of-the-art natural language process (NLP) with their capability of feature learning and representation. As one of the more challenging NLP tasks, neural machine translation (NMT) becomes a new approach to machine translation and generates much more fluent results compared to statistical machine translation (SMT). However, SMT is usually better than NMT in translation adequacy and word coverage. It is therefore a promising direction to combine the advantages of both NMT and SMT. In this article, we propose a deep neural network--based system combination framework leveraging both minimum Bayes-risk decoding and multi-source NMT, which take as input the N-best outputs of NMT and SMT systems and produce the final translation. In particular, we apply the proposed model to both RNN and self-attention networks with different segmentation granularity. We verify our approach empirically through a series of experiments on resource-rich Chinese⇒English and low-resource English⇒Vietnamese translation tasks. Experimental results demonstrate the effectiveness and universality of our proposed approach, which significantly outperforms the conventional system combination methods and the best individual system output.