Limited-angle computed tomography (LACT) offers the advantages of reduced radiation dose and shortened scanning time. Traditional reconstruction algorithms exhibit various inherent limitations in LACT. Currently, most deep learning-based LACT reconstruction methods focus on multi-domain fusion or the introduction of generic priors, failing to fully align with the core imaging characteristics of LACT-such as the directionality of artifacts and directional loss of structural information, which are caused by the absence of projection angles in certain directions. Inspired by the theory of visible and invisible singularities, taking into account the aforementioned core imaging characteristics of LACT, we propose a Visible Singularities Guided Correlation network for LACT reconstruction (VSGC). The design philosophy of VSGC consists of two core steps: First, extract VS edge features from LACT images and focus the model's attention on these VS. Second, establish correlations between the VS edge features and other regions of the image. Additionally, a multi-scale loss function with anisotropic constraint is employed to constrain the model to converge in multiple aspects. Finally, qualitative and quantitative validations are conducted on both simulated and real datasets to verify the effectiveness and feasibility of the proposed design. Particularly, in comparison with alternative methods, VSGC delivers more prominent performance in small angular ranges, with the PSNR improvement of 2.45 dB and the SSIM enhancement of 1.5\%. The code is publicly available at https://github.com/yqx7150/VSGC.