While economic growth is a constant topic to economists, research on economic growth in the global leastdeveloped regions—Sub-Saharan Africa (SSA) countries is of particular theoretical and practical implications.Based on the 1985- 2015 sample data of 102 countries including 26 SSA countries, this paper empirically analyzesthe convergence of economic growth in SSA countries. First, there is a convergence of conditions between countrieswithin the SSA region, i.e. countries with lower per capita income have relatively high economic growth rates aftercontrolling for technological progress rates, savings rates, human capital, population growth rates and depreciationrates. Secondly, there is also conditional convergence on a global scale, i.e. the per capita income of SSA countriesconverges conditionally to that of other richer countries. But when the per capita income of SSA countries reachesa level of 20% of the average per capita income of countries in the rest of the world, the condition will be offset.Thirdly, after controlling for institutional variables such as government stability, democratic accountability, lawand social order, although the bottleneck value of convergence between SSA countries and other countries has notdisappeared, the neck value has been significantly relaxed, and its per capita income will not stop until it reaches 35%of the average per capita income in the rest of the world. These results show that the "late-development advantage" ofbackward countries or regions to achieve economic catch-up is phased, and the improvement of business environmentand other institutional factors can prolong the duration of late-development advantage. The research of this paperhas certain guiding significance for China to win the battle against poverty in 2020 and realize the building of amoderately prosperous society in all respects.