A climbing elevator system has an elevator shaft and an elevator car, a lifting platform, and a supporting device, wherein, in the course of different construction phases of a building, the lifting platform can be anchored at various positions within the elevator shaft. A protective roof is arranged above components of the lifting platform that are to be protected, such as a drive machine. The protective roof has a central roof structure and a peripheral flank structure that has flank walls fixed to the lateral edges of the central roof structure and project outwardly from the central roof structure at an angle with respect to the horizontal. Because of the inclined arrangement of the flank walls, the flank structure can better withstand falling objects and better protect components located underneath. Cantilevered edge regions of the flank walls can be supported on side walls of the elevator shaft.