The African continent has shown great potential in terms of natural resources abundance coupled with a poor economic performance following the assumption "Africa is rich, but Africans are poor" (Tiba and Frikha, 2018). In this background, and compared to the emerging discussions about the resources curse issue, we attempt to investigate this controversial question by supposing the non-linearity of this relationship for 21 Sub-Saharan countries during the spanning of 1990-2015. For this purpose, we employ the PSTR model to determine the threshold above which the resources abundance exerts a detrimental effect on the economic performance of the African economy. Our empirical fact assumes the non-linearity of this relationship. Our facts confirm a negative impact of the natural resources on the growth for both regimes, assuming the validity of the resources curse hypothesis. Also, we estimate the threshold between the resources-blessing and the resources-curse regime. From this perspective, this region is invited to enhance its institutional framework and the institutional tools to minimize the ineffectiveness of its institution to manage the resources revenue adequately.