The need for a knowledge-based society has perpetuated an increasing demand for higher education around the globe. Recently, there has been an increase in the demand for Computer Science professionals due to the rise in the use of ICT in the business, health and education sector. The enrollment numbers in Computer Science undergraduate programmes are usually high, but unfortunately, many of these students drop out from or abscond these programmes, leading to a shortage of Computer Science professionals in the job market. One way to diminish if not completely eradicate this problem is to identify students who are at risk of dropping out and provide them with special intervention programmes that will help them to remain in their programmes till graduation. In this paper, data mining techniques were used to build predictive models that can identify student dropout in Computer Science programmes, more specifically focusing on freshmen attrition since a significant number of dropout occurs in the first year of university studies. The predictive models were built for three stages of the first academic year using five classification algorithms which were Random Forest, Decision Tree, Naïve Bayes, Logistic Regression, and K-Nearest Neighbour. The models used past five years of institutional data stored in university's repositories. Results show that the Naïve Bayes model performed better in stage 1 with an AUC of 0.6132 but in stages 2 and 3, the overall performance of the Logsitic Regression models were better with an AUC of 0.7523 and 0.8902, respectively.