This paper addresses the super-resolution problem for low quality cartoon videos widely distributed on the web, which are generated by downsampling and compression from the sources. To effectively eliminate the compression artifacts and meanwhile preserve the visually salient primitive components (e.g., edges, ridges and corners), we propose an adaptive regularization method depending on the degradation grade of each frame, followed by learning-based pair matching to further enhance the primitives in the upsampled frames. In addition, temporal consistency is considered a directive constraint in both the regularization and enhancement processes. Experimental results demonstrate our solution achieves a good balance between artifacts removal and primitive enhancement, providing perceptually high quality super-resolution results for various web cartoon videos.