Suppose that M is compact, complex (or stable-complex) manifold on which an abelian group T acts. The famous Atiyah-Bott fixed point theorem says that the index of its associated twisted Dolbeault-Dirac operator can be calculated by localizing to an abelian group T acts. The famous Atiyah-Bott fixed point theorem says that the index of its associated twisted Dolbeault-Dirac operator can be calculated by localizing to the T-fixed points of M. In this talk, I will deduce a revised version of Atiyah-Bott theorem. By re-organizing the contribution of T-fixed point sets, the index of the associated Dirac operator will involve both the T-fixed part and pre-image of 0 of certain maps (indeed moment map). As an application, this revised Atiyah-Bott theorem will give an elementary proof to quantization commutes with reduction theorem.