Single image reflection removal (SIRR) is an extremely challenging, ill-posed problem with many application scenarios. In recent years, massive deep learning-based methods have been proposed to remove undesirable reflections from a single input image. However, these methods lack interpretability and do not fully utilize the intrinsic physical structure of reflection images. In this paper, we propose a content and gradient-guided deep network (CGDNet) for single image reflection removal, which is a full-interpretable and model-driven network. Firstly, using the multi-scale convolutional dictionary, we design a novel single image reflection removal model, which combines the image content prior and gradient prior information. Then, the model is optimized using an optimization algorithm based on the proximal gradient technique and unfolded into a neural network, i.e., CGDNet. All the parameters of CGDNet can be automatically learned by end-to-end training. Besides, we introduce a reflection detection module into CGDNet to obtain a probabilistic confidence map and ensure that the network pays attention to reflection regions. Extensive experiments on four benchmark datasets demonstrate that CGDNet is more efficient than state-of-the-art methods in terms of both subjective and objective evaluations. Code is available at https://github.com/zynwl/CGDNet.