Over the past decade, nonlinear image compression techniques based on neural networks have been rapidly developed to achieve more efficient storage and transmission of images compared with conventional linear techniques. A typical non-linear technique is implemented as a neural network trained on a vast set of images, and the latent representation of a target image is transmitted. In contrast to the previous nonlinear techniques, we propose a new image compression method in which a neural network model is trained exclusively on a single target image, rather than a set of images. Such an overfitting strategy enables us to embed fine image features in not only the latent representation but also the network parameters, which helps reduce the reconstruction error against the target image. The effectiveness of our method is validated through a comparison with conventional image compression techniques in terms of a rate-distortion criterion.