This study analyses the effect of oil rents on economic growth in oil exporting African countries. It also attempts to provide both theoretical and empirical analysis of the channels of transmission of resource curse of natural resources on growth in these countries. It adopts a panel data regression analysis for the period 1970 to 2000 for 47 oil exporting countries including Africa, and 13 non-oil exporting countries. The major findings are that there was evidence of resource curse in oil exporting countries, including oil exporting African countries, exchange rate and the Dutch disease syndrome do not explain the resource curse in these countries, including Africa, the absence of democracy in oil exporting countries hinders economic growth, and the despicable state of institutions in oil exporting countries encourage grabbing of public resources and oil rents through rent seeking hence retarding economic growth. The basic conclusion from this study is that for oil exporting African countries, as for other oil exporting countries, oil rents have failed to promote growth.