In order to test convex aspheric surfaces without the aid of other null optics, a novel method combined sub-aperture stitching and interferometry called SSI (sub-aperture stitching interferometry) is introduced. In this letter, the theory, basic principle, and flow chart of SSI are researched. A synthetical optimization stitching mode and an effective stitching algorithm are established based on homogeneous coordinate's transformation and simultaneous least-squares fitting. The software of SSI is devised, and the prototype for testing of large aspheres by SSI is designed and developed. The experiment is carried out with five subapertures for a convex silicon carbide (SIC) aspheric mirror with a clear aperture of 130 mm. The peak-to-valley (PV) and root-mean-square (RMS) error are 0.186 \lambda and 0.019 \lambda, respectively. For the comparison and validation, the TMA system which contained the convex asphere is tested by interferometry. The wavefront error of the central field of the optical system is 0.068 \lambda RMS which approaches to diffraction limitation. The results conclude that this technique is feasible and accurate. It enables the non-null testing of aspheric surfaces especially for convex aspheres.