A new method for testing aspheric surfaces by annular subaperture stitching interferometry is introduced. It can test large-aperture and large-relative-aperture aspheric surfaces at high resolution, low cost, and high efficiency without auxiliary null optics. The basic principle of the method is described, the synthetical optimization stitching model and effective algorithm are established based on simultaneous least-square fitting. A hyperboloid with an aperture of 350 mm is tested by this method. The obtained peak-to-valley (PV) and root-mean-square (RMS) values of the surface error after stitching are 0.433'lambda' and 0.052'lambda' ('lambda' is 632.8 nm), respectively. The reconstructed surface map coincides with the entire surface map from null test, and the difference of PV and RMS errors between them are 0.031'lambda' and 0.005'lambda', respectively. This stitching model provides another quantitive method for testing large aspheric surfaces besides null compensation.