Elevator rope for high-rise building is excited forcibly by the displacements of the building induced by wind forces. The approximate solution of forced vibration of a rope with time-varying length and having a linear damping is presented, on the assumption that the rope tension and the moving velocity is constant, and damping coefficient of the rope is small. Virtual sources of waves which can be assigned to reflecting waves are used for obtaining the approximate solution. Finite difference analyses of the rope vibration are also performed to verify the validity of this approximate solution. The calculated results of finite difference analyses are in fairly good agreement with the calculated results of the approximate solution. The effect of moving velocity and damping factor on the maximum rope deflection are quantitatively made clear.