Membrane structures are sensitive to wind loads and generate large vibrational displacements under wind loads, while the wind-resistant design of membrane structures lacks support from reliability theory. The random vibration model and reliability theory of membrane structures under wind load can provide a reference for the wind-resistant design of membrane structures. The skeleton-supported saddle membrane structure is taken as the object. Based on Von Karman’s large deflection theory and potential flow theory, the theoretical model of random vibration under wind load is established, and the approximate theoretical formula of wind-induced dynamic response is obtained using the perturbation method combined with MATLAB software. In accordance with the first-passage failure criterion of displacement, the reliability performance function of the skeleton-supported saddle membrane structure is established, and the reliability index and failure probability are obtained by means of the first-order second-moment method. The wind tunnel test of the skeleton-supported saddle membrane structure is conducted, and the vibration law at each point of the membrane is analyzed in terms of flow velocity and pressure. The percentage difference is introduced to compare the theoretical results with the experimental results, and the sensitivity analysis of the parameters affecting the reliability is carried out. The results show that the theoretical results are in good agreement with the experimental results. The rise-span ratio, pretension and wind speed all have a certain influence on the reliability of membrane structures. However, an examination of the trend of failure probability indicates that the rise-span ratio exerts a more substantial influence on the reliability of membrane structures than other variables.