Due to the absorption and scattering effects of light in water bodies and the non-uniformity and insufficiency of artificial illumination, underwater images often present various degradation problems, impacting their utility in underwater applications. In this paper, we propose a model-based underwater image simulation and learning-based underwater image enhancement method for coping with various degradation problems in underwater images. We first derive a simplified model for describing various degradation problems in underwater images, then propose a model-based image simulation method that can generate images with a wide range of parameter values. The proposed image simulation method also comes with an image-selection part, which helps to prune the simulation dataset so that it can serve as a training set for learning to enhance the targeted underwater images. Afterwards, we propose a convolutional neural network based on the encoder-decoder backbone to learn to enhance various underwater images from the simulated images. Experiments on simulated and real underwater images with different degradation problems demonstrate the effectiveness of the proposed underwater image simulation and enhancement method, and reveal the advantages of the proposed method in comparison with many state-of-the-art methods.