Abstract: Grey system is a theory which studies poor information specially and it possesses wide suitability. We analyzed the building method of background value in grey model MGM(1,n) and put forward a method of reconstructing background value based on vector continued fractions theory by using rational interpolation, trapezoidal rule in numerical integration and extrapolation formula and built multi-variable non-equidistance grey model MGM(1,n). This model can be used in equidistance and non-equidistance model. It enlarges the scope of application and advances the model’s fitting precision and prediction precision. Examples validate the practicability and reliability of the proposed model.