Low competence of Tanzania's university graduates in the labour market has prompted debate on „falling quality of higher education‟. This article delineates the ideal attributes of quality of higher education and how to pursue these through measures including management effectiveness, competence of academic staff, admission and assessment standards, quality of teaching and learning environment and research. Also, more emphasis has to be given to the two-way university-industry linkages in order to enhance innovations and relevance of higher education to the developmental needs of society through university research. National and institution-based quality assurance mechanisms have been set up to oversee academic standards of the HEIs (universities in particular). Yet quality issues are still being raised. It is contended that improved pre-university quality, including in the medium of instruction will greatly ease the burden on HEIs in addressing issues of quality. Quality assurance measures need to be strengthened in view of the current and emerging global and regional competitiveness challenges.