Motivation: Protein contacts contain key information for the understanding of protein structure and function and thus, contact prediction from sequence is an important problem. Recently exciting progress has been made on this problem, but the predicted contacts for proteins without many sequence homologs is still of low quality and not extremely useful for de novo structure prediction. Method: This paper presents a new deep learning method that predicts contacts by integrating both evolutionary coupling (EC) and sequence conservation information through an ultra-deep neural network formed by two deep residual neural networks. The first residual network conducts a series of 1-dimensional convolutional transformation of sequential features; the second residual network conducts a series of 2-dimensional convolutional transformation of pairwise information including output of the first residual network, EC information and pairwise potential. By using very deep residual networks, we can model very complex relationship between sequence and contact map as well as long-range interdependency between contacts and thus, obtain high-quality contact prediction. Results: Our method greatly outperforms existing contact prediction methods and leads to much more accurate contact-assisted protein folding. Tested on the 105 CASP11 targets, 76 CAMEO test proteins and 398 membrane proteins, the average top L long-range prediction accuracy obtained our method, the representative EC method CCMpred and the CASP11 winner MetaPSICOV is 0.47, 0.21 and 0.30, respectively; the average top L/10 long-range accuracy of our method, CCMpred and MetaPSICOV is 0.77, 0.47 and 0.59, respectively. Ab initio folding using our predicted contacts as restraints can yield correct folds (i.e., TMscore>0.6) for 203 of the 579 test proteins, while that using MetaPSICOV- and CCMpred-predicted contacts can do so for only 79 and 62 of them, respectively. Further, our contact-assisted models also have much better quality than template-based models (especially for membrane proteins). Using our predicted contacts as restraints, we can (ab initio) fold 208 of the 398 membrane proteins with TMscore>0.5. By contrast, when the training proteins of our method are used as templates, homology modeling can only do so for 10 of them. One interesting finding is that even if we train our prediction models with only non-membrane proteins, our method works very well on membrane protein contact prediction. In the recent blind CAMEO benchmark, our method successfully folded one mainly-beta protein of 182 residues, one alpha+beta protein of 125 residues, one mainly-alpha protein of 140 residues and one mainly-alpha protein of 217 residues, all of which have a novel fold and only 0.3L-2.3L effective sequence homologs.