With the rapid development of higher education, the evaluation of the academic growth potential of universities has received extensive attention from scholars and educational administrators. Although the number of papers on university academic evaluation is increasing, few scholars have conducted research on the changing trend of university academic performance. Because traditional statistical methods and deep learning techniques have proven to be incapable of handling short time series data well, this paper proposes to adopt topological data analysis (TDA) to extract specified features from short time series data and then construct the model for the prediction of trend of university academic performance. The performance of the proposed method is evaluated by experiments on a real-world university academic performance dataset. By comparing the prediction results given by the Markov chain as well as SVM on the original data and TDA statistics, respectively, we demonstrate that the data generated by TDA methods can help construct very discriminative models and have a great advantage over the traditional models. In addition, this paper gives the prediction results as a reference, which provides a new perspective for the development evaluation of the academic performance of colleges and universities.