Based on the GM(1,1) direct modeling method and the step by step optimum direct modeling method of GM(1,1) , we put forward a new step by step optimum direct modeling method for the arbitrary time distance grey exponential sequence, prove that the convergence rate of the step by step optimum direct modeling method of GM(1,1) is linear, and the new method have the monotone consistency, convex consistency, and linear transformation consistency. Finaly there are indication that the new method have gradual appr...