Image representation is critical for many visual tasks. Instead of representing images discretely with 2D arrays of pixels, a recent study, namely local implicit image function (LIIF), denotes images as a continuous function where pixel values are expansion by using the corresponding coordinates as inputs. Due to its continuous nature, LIIF can be adopted for arbitrary-scale image super-resolution tasks, resulting in a single effective and efficient model for various up-scaling factors. However, LIIF often suffers from structural distortions and ringing artifacts around edges, mostly because all pixels share the same model, thus ignoring the local properties of the image. In this paper, we propose a novel adaptive local image function (A-LIIF) to alleviate this problem. Specif- ically, our A-LIIF consists of two main components: an encoder and a expansion network.