Residue-residue distance information is useful for predicting tertiary structures of protein monomers or quaternary structures of protein complexes. Many deep learning methods have been developed to predict intra-chain residue-residue distances of monomers accurately, but few methods can accurately predict inter-chain residue-residue distances of complexes. We develop a deep learning method CDPred (i.e., Complex Distance Prediction) based on the 2D attention-powered residual network to address the gap. Tested on two homodimer datasets, CDPred achieves the precision of 60.94% and 42.93% for top L/5 inter-chain contact predictions (L: length of the monomer in homodimer), respectively, substantially higher than DeepHomo’s 37.40% and 23.08% and GLINTER’s 48.09% and 36.74%. Tested on the two heterodimer datasets, the top Ls/5 inter-chain contact prediction precision (Ls: length of the shorter monomer in heterodimer) of CDPred is 47.59% and 22.87% respectively, surpassing GLINTER’s 23.24% and 13.49%. Moreover, the prediction of CDPred is complementary with that of AlphaFold2-multimer.