Content-based image retargeting is a technique that resizes an input image to a given target resolution while minimizing distortions of important objects caused by aspect ratio variations. Conventional approaches have shared a similar methodology which aims to preserve salient regions as much as possible while allowing distortions of less important regions. Those methods have shown satisfactory results for input images whose objects are distinct and backgrounds are monotonous. However, their performance is not always guaranteed for images containing structural components such as straight lines, which are prone to be distorted after resizing and sensitive to human visual perception. In this paper, we propose a structure-aware axis-aligned grid deformation approach for robust image retargeting. Based on axis-aligned grid, our method finds the optimal grid for target image by quadratic optimization represented by two objective functions. The first one is the As-similar-as-possible (ASAP) energy function, which aims to preserve important regions while allowing distortions of trivial regions. The second one is the Adaptive Laplacian regularization (ALR) energy function, which aims to relieve structural distortions. Those two energy functions are combined into single quadratic optimization model ensuring the global convexity and solved by a quadratic programming solver for finding the optimal grid. Experimental results show that our method is robust to structural distortions while achieving the basic purpose of content-based image retargeting. For objective comparisons with other methods, we have provided objective evaluation scores by using a recent state-of-the-art image retargeting quality assessment scheme.