An elevator in a high-rise building causes a problem of elevator rope sway. To address this problem, it is necessary to understand the relation between responses of a building and rope. In this study, earthquake ground motions are synthesized with a newly proposed simple method to construct a Fourier phase spectrum. The response of a building-elevator system is obtained using a response spectrum and complex eigenvectors, which can consider non-proportional damping. Seismic risk of elevator rope is evaluated for 50, 100, 150, 200 and 250-meter-high buildings. As a result, the probability of rope damage changes significantly depending on the height of a building and an elevator car position. It is recommended to move and park an elevator car at low risk positions when few people use the elevator such as in nighttime.