Prediction of protein backbone torsion angles (Psi and Phi) can provide important information for protein structure prediction and sequence alignment. Existing methods for Psi-Phi angle prediction have significant room for improvement. In this paper, a new deep residual inception network architecture, called DeepRIN, is proposed for the prediction of Psi-Phi angles. The input to DeepRIN is a feature matrix representing a composition of physico-chemical properties of amino acids, a 20-dimensional position-specific substitution matrix (PSSM) generated by PSI-BLAST, a 30-dimensional hidden Markov Model sequence profile generated by HHBlits, and predicted eight-state secondary structure features. DeepRIN is designed based on inception networks and residual networks that have performed well on image classification and text recognition. The architecture of DeepRIN enables effective encoding of local and global interatcions between amino acids in a protein sequence to achieve accruacte prediction. Extensive experimental results show that DeepRIN outperformed the best existing tools significantly. Compared to the recently released state-of-the-art tool, SPIDER3, DeepRIN reduced the Psi angle prediction error by more than 5 degrees and the Phi angle prediction error by more than 2 degrees on average. The executable tool of DeepRIN is available for download at http://dslsrv8.cs.missouri.edu/~cf797/MUFoldAngle/.