Poisson noise appears in various imaging applications, such as low-light photography, medical imaging and space imaging. In many cases we may have occlusions in the received image in addition to the noise. Thus, the problem of Poisson denoising turns to be a Poisson inpainting one in which we need both to remove the noise and recover the values in the occluded locations. In this work we extend a recent novel Poisson denoising method for the task of image inpainting. To the best of our knowledge this is the first work that deals with the problem of Poisson inpainting.