Intra-protein residue-level contact prediction has drawn a lot of attentions in recent years and made very good progress, but much fewer methods are dedicated to inter-protein contact prediction, which are important for understanding how proteins interact at structure and residue level. Direct coupling analysis (DCA) is popular for intra-protein contact prediction, but extending it to inter-protein contact prediction is challenging since it requires too many interlogs (i.e., interacting homologs) to be effective, which cannot be easily fulfilled especially for a putative interacting protein pair in eukaryotes. We show that deep learning, even trained by only intra-protein contact maps, works much better than DCA for inter-protein contact prediction. We also show that a phylogeny-based method can generate a better multiple sequence alignment for eukaryotes than existing genome-based methods and thus, lead to better inter-protein contact prediction. Our method shall be useful for protein docking, protein interaction prediction and protein interaction network construction.