An important determinant of a good tertiary institution is the academic performance of its students and the results produced. Research had revealed some factors as contributing to the academic performance of students. This research hence used the available factors to develop a framework that can be used by decision-makers to predict the academic performance of prospective postgraduate students. This study hence aims at developing a model that predicts postgraduate students’ performance using decision tree algorithms.Dataset used in this study was gotten from the postgraduate school, the University of Ibadan, and her Computer Science department. The datasets were adequately pre-processed and major attributes contributing to the prediction of postgraduate students' performance were determined using seven (7) different ranking evaluators. RandomTree, RepTree and J48 decision tree algorithms were applied to the pre-processed dataset, and rules were generated from the optimal algorithm.The results indicated the best attributes for predicting postgraduate students’ performance. It also showed that students from Federal undergraduate schools were more likely to finish their postgraduate course with a Ph.D. grade than their counterparts from state and private schools. J48 algorithm proved to be a better predictor for an imbalanced dataset while the RandomTree algorithm outperforms J48 when considering a balanced dataset.To improve the predictive ability of this model, more datasets containing information from the prospective students should be collected which should include students’ sociological background, personality, expectations as well as previous academic performances. Other data mining methods such as Naïve Bayes, Neural Network, and Support Vector Machine can be trained on the datasets and their results compared for better predictive models.