Survival analysis with genomics data provides a deep understanding of biological processes related to prognosis and disease progression at the molecular level. However, high-dimensional small sample genome data causes computational challenges in survival analysis. To address this problem of overfitting and poor interpretation of existing models, we applied the deep learning technology to genome data and proposed a survival analysis model based on an image-based residual neural network model, called Cox-ResNet. High-dimensional gene expression data was embedded into 2D images according to gene positions on chromosomes, and then a residual network model based on Cox proportional hazards was introduced to perform survival analysis. We demonstrated the performance of Cox-ResNet on five datasets of different cancer types from TCGA, comparing it with the cutting-edge survival analysis methods. The Cox-ResNet model not only shows better performance in prediction accuracy, but also biologically interpretable, by generating heat-maps and prognostic genes for high-risk groups with the guided Grad-Cam visualization method. By performing protein-protein interaction network analysis, we examined hub genes and their biological functions for the bladder cancer. These findings confirm that Cox-ResNet model provides a new solution for discovering the driver genes of poor cancer prognosis.