The relationship between globalization and economic growth, especially in the poorer developing countries, is controversial. Many previous studies have used single globalization indicators such as the ratio of exports plus imports to GDP. This paper uses a comprehensive measure of a globalization of Dreher (2006), which is based on measures of globalization of the economic, social and political sectors. Panel data estimates with data of 21 low income African countries show a small but significant positive permanent growth effects. The sensitivity of this growth effect is examined with the extreme bounds analysis (EBA). Contrary to the findings by Levine and Renelt (1992) that cross country growth relationships are fragile, the effects of globalization and some other determinants of the long run growth rate are found to be robust by EBA.