Demand for university education has increased due to the recent innovations of universal, free and compulsory education at the basic and senior secondary education level. Education has been expanding very rapidly at all levels in Nigeria. However, there are serious problems related to quality, equity, unavailable human and material resources and access. Some of these problems are related to the fact that formal education was introduced to the different regions in Nigeria at different time, and the nation's focus was more on the basic education, without building a strong framework for the higher education that could provide the necessary policies committed to equity, access, quality and efficiency. The data on admissions and enrolments were obtained from the Federal Bureau of Statistics and National Universities Commission and Joint Admission and Matriculation Board's websites. The paper analysed the pattern of access based on the six geo-political zones in Nigeria, gender, and academic disciplines using percentage, mean and chart. The impact of some major factors such as admission policy and finance on access to university education were also examined. The findings revealed that access to university education in Nigeria when compared with the number of qualified applicants was low. There was disparity in access across regional zones and there exists differences in the access of male and female all-over the country. Also, there was gap in access across disciplines. In addition, funding of the universities was state-supply model and this has restricted expansion of the institutions for more access. Furthermore, admission policy has impact on the rate of access to university education in Nigeria. Based on the disparity observed in access to university education in Nigeria, it was suggested that a coercive attention and affirmative action in terms of adequate funding and dynamic policy on admission are needed to address the situation. (Contains 6 tables and 5 figures.)