The lateral support structure of a large aperture primary mirror was researched and optimized to effectively reduce the deformation of the primary mirror under the gravity. First, an idea and criterion to optimize the edge-lateral support structure was provided theoretically.Then, on the basis of the tangential shearing support principle, the optimization procedure of the support structure and its merit were explained. Based on the principle, a lightweight mirror with a diameter of 2 060 mm was taken as an example, and an equal-angle lateral support was optimized by using 16 discrete points. According to the characteristic of the lightweight mirror, the original supporting structure was improved to be the no-equal-angle lateral support to avoid the disadvantage that the gap between the support forces was large in previous structure. The results indicate that the supporting stiffness of the system has been enhanced and the mirror deformation is reduced from 1.723 nm to 1.633 nm. It concludes that the edge tangential shearing support structure which is fit to the lightweight mirror with sector hole can keep the mirror surface figure to a large extent. So this method provides a new option for the lateral support of large-aperture lightweight mirror.