Permeability is a critical parameter for understanding subsurface fluid flow behavior, managing reservoirs, enhancing hydrocarbon recovery, and sequestering carbon dioxide. In general, permeability is measured in the laboratory based on subsurface core samples, calculated from well logs or estimated from well tests. However, laboratory measurements and well tests are expensive, time-consuming, and usually limited to a few core samples or wells in a hydrocarbon field or carbon storage site. Machine-learning techniques are good options for generating a rapid, robust, and cost-effective permeability prediction model because of their strengths to recognize the potential interrelationships between input and output variables. Convolutional neural networks (CNN), as a good pattern recognition algorithm, are widely used in image processing, natural language processing, and speech recognition, but are rarely used with regression problems and even less often in reservoir characterization. We have developed a CNN regression model to estimate the permeability in the Jacksonburg-Stringtown oil field, West Virginia, which is a potential carbon storage site and enhanced oil recovery operations field. We also evaluate the concept of the geologic feature image, which is converted from geophysical well logs. Five variables, including two commonly available conventional well logs (the gamma rays [GRs] and bulk density) and three well-log-derived variables (the slopes of the GR and bulk density curves, and shale content), are used to generate a geologic feature image. The CNN treats the geologic feature image as the input and the permeability as the desired output. In addition, the permeability predicted using traditional backpropagation artificial neural networks, which are optimized by genetic algorithms and particle swarm optimization, is compared with the permeability estimated using our CNN. Our results indicate that the CNN regression model provides more accurate permeability predictions than the traditional neural network.