Abstract: GM (1, 1) model is suitable for the series with exponential growth and small fluctuation, but the prediction accuracy of the series with parabolic or saturated development trends is not high. Parabolic growth sequences are widely found in practical problems. For example, the annual GDP of some provinces in China grew rapidly in the early stage but slowed down in the later stage, presenting a parabolic or saturated development trend. In order to improve the prediction effect of grey model on exponential and parabolic sequences, the sum of a quadratic polynomial and GM (1, 1) model is proposed as a new model (NRGM (1, 1)). Furthermore, the matrix model (MINRGM (1, 1)) of NRGM (1, 1) is proposed, which is directly applicable to interval number sequences. The prediction formula of the model is obtained based on Cramer's law. The MINRGM (1, 1) model is used to forecast China's railway passenger volume, civil aviation passenger volume, total passenger volume, and the GDP of Hebei province, and the GDP of Hebei province presents a parabolic development trend. Compared with the competition models, the MINRGM (1, 1) model achieves better prediction results.