Spherical inflatable membrane structures are extremely prone to suffer aeroelastic instability under strong winds, which requires detailed investigation. In this paper, based on the digital image correlation technology (DIC), the displacement and strain response characteristics under wind loads are investigated. Furthermore, the aeroelastic instability characteristics and the criteria for determining the occurrence of this phenomenon are defined. The results show that the top, windward, and side parts of the structure deform upward, inward, and outward. The extreme value of the total displacement occurs at approximately 1/2 of the windward region. Maximum principal strains occur at the windward and leeward centers together with the top region. After the wind speed exceeds the critical value (the dimensionless critical wind speed is observed at 1.37), the structure undergoes a sudden change of dominant vibration mode, the damping ratio decreases dramatically and reaches nearly zero. It can be concluded that the aeroelastic instability of the spherical inflatable membrane structure is caused by vortex-induced resonance and is characterized by a sudden increase in deformation and amplitude, a sudden change of the dominant vibration mode, and a rapid decay of the damping ratio. The Reynolds number after reaching the instability critical wind speed is Re > 3.1 × 105.