According to the error problem of grey prediction models calculating non-homogenous index sequences, the whitenization differential equation and the parameter unbiased estimation method are discussed. Firstly, the different forms of the existed non-homogeneous grey prediction model are proved, and the basic form of NGM(1,1,k) is built. Then two kinds of unbiased basic form of NGM(1,1,k) are proposed from two aspects which are grey derivative optimization and background value optimization. The direct modeling method of unbiased NGM(1,1,k) is constructed by verifying the unity of the two models, and the whitenization index repeatability of this method is proved. Finally, the rationality and effectiveness of the model are verified by two examples which are the fitting of six types of data and the total amount simulation of natural gas supply in Nanjing.