The higher the level of development of higher education, the larger its contribution to socioeconomic development. In order to predict the trend of higher education development in a country more accurately, a new methodology is employed in this study. A weakening buffer operator-based GM (1, 1) model is constructed using Kazakhstan's gross enrollment rate (GER) of higher education as the subject of study, which eliminates the disturbance of the shock perturbation system and increases prediction accuracy. Seven models with varying sample sizes are constructed. It is discovered that the short sequence prediction model outperforms the long sequence prediction model. To demonstrate the superiority of the proposed method, cubic curves and logistic models are chosen for comparison. The results of the study revealed that the cubic curve has a better fitting, but the prediction results are overly large due to the quick growth rate of the recent raw data, which is not in line with the realistic development; the logistic model has poor fitting and cannot be used for prediction; the buffer operator-based GM (1, 1) model can effectively deal with the issue of missing data or data outliers, and provide accurate predictions of the trend of higher education development. When compared to other methods, the proposed method is more practicable, reliable, and superior.