Increasing the image quality of positron emission tomography (PET) is an essential topic in the PET community. For instance, thin-pixelated crystals have been used to provide high spatial resolution images but at the cost of sensitivity and manufacture expense. In this paper, we proposed an approach to enhance the PET image resolution and noise property for PET scanners with large pixelated crystals. To address the problem of coarse blurred sinograms with large parallax errors associated with large crystals, we developed a data-driven, single-image super-resolution (SISR) method for sinograms, based on the novel deep residual convolutional neural network (CNN). Unlike the CNN-based SISR on natural images, periodically padded sinogram data and dedicated network architecture were used to make it more efficient for PET imaging. Moreover, we included the transfer learning scheme in the approach to process cases with poor labeling and small training data set. The approach was validated via analytically simulated data (with and without noise), Monte Carlo simulated data, and pre-clinical data. Using the proposed method, we could achieve comparable image resolution and better noise property with large crystals of bin sizes of thin crystals with a bin size from to . Our approach uses external PET data as the prior knowledge for training and does not require additional information during inference. Meanwhile, the method can be added into the normal PET imaging framework seamlessly, thus potentially finds its application in designing low-cost high-performance PET systems.