In order to satisfy high precision and fast optical surface measuring, an iterative algorithm for annular subaperture stitching is discussed based on the Subaperture Stitching and Localization (SASL) algorithm. The basic theory of annular subaperture stitching is introduced, which can be divided into two parts, one is how to determine the overlapping points precisely and the other is how to find optimal configuration. Then, how to determine the overlapping points in annular subaperture stitching is studied and the detailed procedure of the iterative stitching algorithm is presented. Finally, a paraboloid of 160 mm aperture is tested with Annular Subaperture Test(AST), tested results in PV value of 0.186λ and RMS value of 0.019λ are consistent with the auto-collimated full aperture testing. All these discussions clearly prove that the iterative annular subaperture stitching algorithm can meet the requirement for high precision testing of aspherical surfaces.