When a building with viscoelastic dampers is subjected to wind excitations, its dynamic properties such as vibration period and damping ratio can vary, depending on the frequency contents of the excitation. This is due to frequency sensitivity of the viscoelastic damper, and contradicts with the basis of the conventional spectral or modal analysis method using the constant dynamic properties evaluated at resonant state of the building. This paper points out the need for considering frequency sensitivity of a building when it possesses velocity-dependent dampers such as viscoelastic dampers, and proposes for the first time a new spectral or modal analysis method to predict the wind-induced response, considering the frequency sensitivity of the viscoelastic damper.