Abstract: At present, the DGM(1,1) model has many applications, which makes the model have a lot of improvement in accuracy and robustness. However, for these current applications, the impact of random disturbances on the model is not considered. A white noise is introduced in the traditional DGM(1,1) model by referring to tthe idea of random difference. The iterative method is used to solve the DGM(1,1) model which introduces the white noise sequence, and the corresponding analysis formula is obtained. According to this analysis, different values of β_1 will cause random disturbances to have different effects on the model. The cases with different β_1 values are used for comparative analysis. In the more general case of this model, what will the properties of the model differ after adding the random disturbance? The results show that when |β_1|<1, the variance of the model converges gradually under the influence of random disturbance, and the model is relatively stable, while when |β_1|>1, the variance increases exponentially, and the model is in an unstable state.