The effect of Gaussian white noise on erosion of safe basin (EOSB) in power system is studied in this paper.The studied model is described by the classical single-machine infinite-bus (SMIB) system with the values of parameters at which the safe basin of the clean system is integral.The stochastic Melnikov method is first applied to predict the onset of EOSB when the noise excitation is present in system.And then the eroded basins are simulated according to the necessary restrictions for the systems parameters.It is found that for the noisy power system when the noise intensity σ is greater than a threshold, EOSB occurs and as σ is further increased EOSB is aggravated.These studies imply that random noise excitation can induce and enhance EOSB in power system.