Based on grey system theory, a novel kind of non-equidistant optimum grey model GM(1,1) with optimizing modified the nth component taken as initial value of response function of grey differential equation and reconstructing the background value function to obtain the approximately expressions of parameters of the background value function was proposed, the method of precision inspection was introduced. The example was given. The method can be used for model establishing on equal interval, as well as on non-interval. Moreover, GM(1,1) model’s fitting precision and prediction is advanced and the scope of application is enlarged. The model is simple and practical, and has a generalizing value in metal cutting data process.