Recently deep neural networks have been successfully applied in channel coding to improve the decoding performance. However, the state-of-the-art neural channel decoders cannot achieve high decoding performance and low complexity simultaneously. To overcome this challenge, in this paper we propose doubly residual neural (DRN) decoder. By integrating both the residual input and residual learning to the design of neural channel decoder, DRN enables significant decoding performance improvement while maintaining low complexity. Extensive experiment results show that on different types of channel codes, our DRN decoder consistently outperform the state-of-the-art decoders in terms of decoding performance, model sizes and computational cost.