The background value coefficient α of the non equidistant GM (1, 1) model has great influence on the predictive capability, but it is difficult to determine its optimal value. For these problems, the bacterial foraging algorithm and a GM (1, 1) model were combined and the BFA GM (1, 1) optimization model was proposed. Taking the experiment of empennage fatigue life prediction as an example, the performances of the BFA GM (1, 1) model, the PSO GM (1, 1) model and the GA GM (1, 1) model were analyzed and compared. The results have shown that the BFA GM (1, 1) model consumes the least time and obtains the lowest average prediction error, and that the BFA GM (1, 1) model proposed is competent to find the optimal background value coefficient α quickly and accurately, thereby increasing the empennage fatigue life prediction accuracy under the conditions of “small samples” and “poor information”.