International Journal of Research Studies in Education, 2017; 6 (2): 29-40In recent years, Tanzanian higher learning institutions have attracted many candidates to pursue various postgraduate programmes. However, some higher education stakeholders have echoed their concerns that the number of postgraduate students who successfully graduate from the institutions is low, despite the increase in postgraduate enrollment. Supervisors have consistently been identified by postgraduate students as the main source of either delaying graduation or dropping from the postgraduate studies. This study was conducted in Tanzania, involving 76 academic staff, including 42 males and 34 females, from four public universities and two private universities. The study was designed to achieve two specific objectives: First, to examine the challenges of supervising postgraduate students as experienced by supervisors in Tanzanian higher learning institutions; and secondly, to recommend best practices for improving the supervision of postgraduate students in Tanzanian higher learning institutions. The findings indicated that the supervision of postgraduate students in Tanzanian higher learning institutions faces numerous challenges which could be categorized as student-related and administrative challenges. This calls for collaborative efforts among higher education stakeholders to ensure quality graduates who can contribute significantly to the development of their societies. In view of the findings of this study, it is recommended, among others, that the higher learning institutions should improve administrative and support services to enable both supervisors and supervisees perform their responsibilities effectively.