Annular sub-aperture stitching interferometry (ASSI) has provided an alternative solution to measure rotationally symmetric aspheric surfaces with low cost and high flexibility. It is an effective way to test the aspheric surface with a larger aperture and larger relative aperture without null compensation. In this paper, two kinds of annular sub-aperture stitching algorithms, pairwise sequential stitching (PSS) and global synchronously stitching (GSS), were studied. The detailed mathematical expressions are shown in the form of matrix. Besides, the influence of the noise and number of sub-apertures to the two algorithms was also studied by simulation. At last, experimental results of a convex hyperboloid surface by using the two stitching algorithms are presented.