The collision dynamics of a droplet falling onto a substrate is significant in various applications such as inkjet printing, spray coating, and bioprinting. Generally, several factors, such as the fluid properties (e.g., viscosity or surface tension) and substrate characteristics (e.g., surface roughness or flexibility) govern whether falling droplets spread or splash. In this study, we experimentally investigate droplet collision dynamics on a thin, flexible membrane for various Weber numbers (230<We<600) and membrane stiffnesses, which can be controlled by the applied tensile force. In addition, the effect of membrane vibration on collision behavior is considered. In the high Weber number regime, splashing is dominant, regardless of the membrane stiffness. In contrast, in the low Weber numberregime, a transition between splashing and deposition is observed, depending on the membrane stiffness. In short, flexible membrane vibration induces droplet splashing despite the insufficient kinetic energy of the droplet. Increasing the stiffness of the membrane contributes to the suppression of droplet splashing by minimizing membrane vibration.