In recent years, production technologies for arbitrary-shaped (non-rectangular shaped) displays to improve the appearance of digital photo frames or to increase the advertising effectiveness of digital signs are proposed. To utilize such arbitrary-shaped displays effectively, an image retargeting method is required for converting a rectangular shaped image into an arbitrary-shaped image while preserving the information of the input image. However, conventional image retargeting methods can only convert a rectangular shaped image into a rectangular shaped image with different size or aspect ratio. In this paper, we propose a new image retargeting method for arbitrary-shaped images by dividing the image retargeting problem into two phases: moving important regions and inpainting unimportant regions. In the first phase, we find several important regions from the (rectangular shaped) input image using a block matching procedure. Then, we move these regions to the watching region of the target (arbitrary-shaped) display by minimizing the proposed energy functional with a greedy algorithm. After moving these regions, we inpaint the rest of the image to preserve the consistency with the input image. The experimental results show that we can obtain natural and structure-preserved images with arbitrary-shape by our proposed method.