We investigate a drive-response system by considering the impacts of noise on generalized synchronization (GS).It is found that a small amount of noise can tu the system from desynchronization to the GS state in the resonant case no matter how noise is injected into the system. In the non-resonant case, noise with intensity in a certain range is helpful in building GS only when the noise is injected to the driving system. The mechanism behind the observed phenomena is discussed.