A method is proposed to forecast the catastrophic changes of the states of bistable systems with the use of externally applied Gaussian random force. The prediction is based on the fact that the probability distribution function of the states of a bistable system under the influence of Gaussian random force becomes far from Gaussian in the vicinity of its catastrophe. In other words, the anomalous increase of the variance of the probability distribution function in the vicinity of the catastrophe can be utilized as a precursory phenomenon to predict the catastrophe. The anomaly of the probability distribution function is caused by the nonlinear property of the bistable system.