Sea-surface temperature (SST) images obtained by satellites contain noise and missing SSTs due to cloud covers. We propose a method for reconstructing denoised cloud-free SST images via deep-learning-based image inpainting. For denoizing, we use data-assimilation images to train a reconstruction network by considering the physical correctness of SSTs. For reconstruction stability, we introduce <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">anomaly inpainting network</i> , which does not directly complete missing SSTs but estimates the difference between the unobserved SSTs and the average SSTs. SSTs do not fluctuate much over a few days; thus, we can use recent average SSTs as a rough estimation of SSTs and can assume that the SST difference will be within a specific range. We conducted experiments to evaluate our method with satellite SST images and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> SST data. The results indicate that our method with anomaly inpainting network qualitatively and quantitatively outperformed conventional SST image inpainting methods.