Abstract: Single-layer cylindrical latticed shell (SLCLS) is characterized by its large span, lightweight, and excellent light transmission, making it suitable for sightseeing greenhouses such as ecological parks. However, the SLCLS is associated with low in-plane and out-of-plane stiffness, which can lead to functional damage and structural failure under sudden disasters such as strong snow, wind, or earthquakes. To address these problems, the prestressed cable-supported greenhouse single-layer cylindrical latticed shell (PCGSLCLS) is proposed, which combines SLCLS with flexible prestressed cables. This method is designed to modify the in-plane and out-of-plane stiffness of SLCLS, enhance its overall rigidity, and improve its global stability. Consequently, this method is considered a highly competitive and feasible option to address the afore mentioned problems. Extensive research has been conducted on the form-finding theory, cable force optimization methods, and stability analysis of cable-supported space latticed shells. However, further in-depth research on cable-laying methods for SLCLSs is still required. In the work, the stability performance of PCGSLCLSs is investigated by applying in-plane cable-laying method, linear buckling-based out-of-plane cable-laying method, and nonlinear buckling-based out-of-plane cable-laying method. The proposed linear and nonlinear buckling-based cable-laying methods are based on the displacement proportions of each node derived from linear and nonlinear buckling analyses, which determine the direction and length of struts. Different PCGSLCLSs are formed by varying parameters such as the mesh type of SLCLS (rectangular mesh, diamond mesh, single-diagonal mesh, and double-diagonal mesh), the rise-span ratio of SLCLS (1/6, 1/5, and 1/4), the sag-span ratio (1/20, 1/15, 1/12, and 1/10), and the prestress level of cables (5%, 10%, 15%, and 20%). The general finite element (FE) analysis program ANSYS is utilized to perform full-process elastoplastic buckling analysis. Beam188 element and Link10 element from the element library are employed to simulate the members, cables, and brace struts in PCGSLCLS. Correspondingly, the FE models are established to explore the impact of the prestressed cable-laying on the stability capacity of SLCLSs. The results indicate that there is the most significant increase in the stability capacity of SLCLSs with the rectangular, diamond, and single-diagonal mesh under linear buckling-based cable-laying, with the increase rates of 177.42%, 201.83%, and 95.97%, respectively, except for the rise-span ratio of 1/4. SLCLS with double-diagonal mesh achieves the greatest improvement in stability capacity under nonlinear buckling-based cable-laying, with an increase of 122.59%. The in-plane cable-laying method is found to provide a smaller improvement in stability capacity compared to linear and nonlinear buckling-based cable-laying methods. Among them, the ranges of stability capacity under in-plane and out-of-plane cable-laying are 10.42%-59.63% and 46.79%-201.83% in the different types of SLCLSs, respectively. Regardless of whether prestressed cables are laid, the stability capacity of SLCLSs basically increases with the increase of the rise-span ratio. The stability capacity is also found to increase with the sag-span ratio, with a maximum improvement of 30.30%. In addition, the optimal levels of prestress improve the stability capacity, according to the cable-laying and mesh type of the SLCLSs. The prestressed cable-laying enhance the in-plane and out-of-plane stiffness, as well as the stability performance of SLCLSs. There is a great impact of the cable-laying on the stability capacity of PCGSLCLSs. Suitable cable-laying is proposed for the different SLCLSs. The finding can also provide technical guidance and theoretical references for practical engineering.