In this paper, a modified stitching algorithm for annular subaperture stitching interferometry (ASSI) for aspheric surfaces is proposed. The mathematical model of adjustment error is deduced based on the wavefront aberration theory and rigid body movement; meanwhile, its basic principle and theory are introduced. The modified stitching algorithm is established based on the mathematical model and the simultaneous least-squares method, which keeps the error from transmitting and accumulating. So the adjustment error can be compensated efficiently. In addition, the standard deviation (SD) in the overlapped regions is used as the figure of merit to determine the stitching accuracy. Finally, simulations and experiments are given to verify the validity and rationality of the proposed algorithm. The results show that the introduced method is quite efficient.