The potential growth of small and medium enterprises (SMEs) elsewhere in the world including in Tanzania depends on conducive business environment. However, SMEs in Tanzania are confronted with a number of constraints which hamper their potential growth. This paper aims at assessing business constraints that affect the potential growth of SMEs in Tanzania. Variables such as inadequate business training, insufficient capital, competition, ant-entrepreneurial culture, bureaucratic procedures in business registration, high taxes, technological barrier/backwardness, theft/cheating and lack of trust, poor infrastructure, and corruption that affect potential growth of SMEs were measured. Quantitative approach was used in this study. An intensive literature review was conducted to find out the relationship between the variables. Frequency and percentage were computed to find out the results of the study. The findings show that inadequate business training,insufficient capital and anti-entrepreneurial culture are significant constraints. The study recommends that strategic training programmes need to be designed and implemented in order to provide SMEs with adequate entrepreneurial knowledge, skills and attitude. Additionally, re-engineering of lending schemes by the government and financial institutions is needed in order to enable SMEs access credit.