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Based on the exponential trait of grey model and the definition of integral, the reconstruction method of GM(1, 1) modelpsilas background value of non-equal distance sequence was put forward, the approximately expressions of parameters of the background value function were obtained and a kind of non-equidistant optimum grey model GM(1, 1) to test data process 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) modelpsilas 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.