A new algorithm is proposed for annular subaperture stitching technology based on Hartmann-Shack wavefront sensor. The algorithm can reconstruct the whole-aperture wavefront without reconstructing annular subaperture wavefront. The algorithm is feasible for the limited Hartmann sampling frequency in annular subaperture. By evaluating the sensitivity of the algorithm to the measurement noise of wavefront gradient data, the algorithm is not sensitive to the measurement noise of the wavefront gradient. The algorithm can stitch different abberations except spherical abberations with high precision. There is some defocus aberration in the residual aberration for reconstructing the spherical aberration, the root mean square value (RMS) of residual aberration depends on the RMS of the spherical aberration and it is decreased by removing the coupling error of the spherical aberration.