It is required a large amount samples of fatigue life trial to predict or evaluate the fatigue life of gear. The GM（ 1

1） model can be used in the analysis of a little amount samples of experiments. The theory of GM（ 1

1） model on the grey system is proposed

then the prediction model of GM（ 1

1） on the trial data of fatigue life of a sample of certain bevel gear is carried out. The calculation result shows a higher accuracy to prove the feasibility to predict the test data of fat igue life of the spiral bevel gear applying the grey system theory.