Strong turbulence in the driven drift-wave equation of plasma can be suppressed successfully to a laminar flow by an external periodic signal with proper frequency and strength. In the driving wave coordinates，by transforming the wave system to a set of coupled oscillators (modes) moving in a periodic potential，generalized phase synchronization between these modes is regarded as one of the control mechanisms. In this paper，the effect of noise is studied in the course of the turbulence control. It is found that the laminar flow becomes disordered again with fairly weak bias noise，at the same time the generalized phase synchronization between the modes is lost. However，when the bias noise is quite strong，the quasi-period laminar state can be maintained and the modes can also reach generalized phase synchronization with each other.