Recent image inpainting methods have shown promising results due to the power of deep learning, which can explore external information available from the large training dataset. However, many state-of-the-art inpainting networks are still limited in exploiting internal information available in the given input image at test time. To mitigate this problem, we present a novel and efficient self-supervised fine-tuning algorithm that can adapt the parameters of fully pre-trained inpainting networks without using ground-truth target images. We update the parameters of the pre-trained state-of-the-art inpainting networks by utilizing existing self-similar patches (i.e., self-exemplars) within the given input image without changing the network architecture and improve the inpainting quality by a large margin. Qualitative and quantitative experimental results demonstrate the superiority of the proposed algorithm, and we achieve state-of-the-art inpainting results on publicly available benchmark datasets.