Annular sub-aperture stitching interferometry technology can test steep conformal aspheric surfaces with low cost and high efficiency without auxiliary null optics. The effective splicing algorithm was established based on simultaneous least-squares method and Zernike polynomial fitting. Firstly, the basic principle of the algorithm of the annular sub-aperture stitching was studied. Secondly, the mathematical formulas of the sub-aperture effective area were derived and the parameters of the sub-aperture effective area were calculated and optimized. Finally, the reasonable mathematical model was established. The detection method of annular sub-aperture stitching high steepness aspheric has been tested through on experimental verification. As a result, the surface map of the full aperture after stitching was consistent to the input surface map, the difference of PV error and RMS error between them is 0.015 1λ and 0.004 7λ(λ is 632.8 nm); the PV and RMS of residual error of full aperture phase distribution is 0.043 5λ and 0.005 2λ. The results conclude that this splicing model and algorithm were accurate and feasible.