The Mechanism of grey prediction method and its application advantages in safety prediction were described.This method was used to predict the vibration amplitude within the coming 6hours for a steam turbine.Moreover , the prediction results were examined using correlation degree and posterior error.Results indicated that , this grey prediction method had small posterior error and got a grade I accuracy.We can foreknow the variation trend of vibration amplitude of the steam turbine through this method , so as to take timely countermeasures.Therefore , the operation safety of the power unit was improved. The Mechanism of gray prediction method and its application advantages in safety prediction were described.This method was used to predict the vibration amplitude within the coming 6 hours for a steam turbine. Moreover, the prediction results were examined using correlation degree and posterior error. Results indicate that, this gray prediction method had small posterior error and got a grade I accuracy. we can foreknow the variation trend of vibration amplitude of the steam turbine through this method, so as to take timely countermeasures.Therefore, the operation safety of the power unit was improved.