As a highly ill-posed issue, single-image super-resolution (SISR) has been widely investigated in recent years. The main task of SISR is to recover the information loss caused by the degradation procedure. According to the Nyquist sampling theory, the degradation leads to the aliasing effect and makes it hard to restore the correct textures from low-resolution (LR) images. In practice, there are correlations and self-similarities among the adjacent patches in the natural images. This article considers the self-similarity and proposes a hierarchical image super-resolution network (HSRNet) to suppress the influence of aliasing. We consider the SISR issue in the optimization perspective and propose an iterative solution pattern based on the half-quadratic splitting (HQS) method. To explore the texture with local image prior, we design a hierarchical exploration block (HEB) and progressive increase the receptive field. Furthermore, multilevel spatial attention (MSA) is devised to obtain the relations of adjacent feature and enhance the high-frequency information, which acts as a crucial role for visual experience. The experimental result shows that HSRNet achieves better quantitative and visual performance than other works and remits the aliasing more effectively.