When calculating curved Ricci Flow, non-convergence emerges due to the existence of undersized angles in triangular meshes. Concerning the problem of non-convergence, a Delaunay triangulation subdivision algorithm of spherical convex graph of enhancing the minimum angle was proposed. First of all, the Delaunay triangulation subdivision algorithm of spherical convex graph was given. The proposed algorithm had two key operations:1) if a Delaunay minor arc was "encroached upon", a midpoint of the Delaunay minor arc was added to segment the Delaunay minor arc; 2) if there was a "skinny" spherical triangle, it was disassembled by adding the center of minor circle of its circumscribed sphere. Then, the convergence criteria of the proposed algorithm was explored on local feature scale and an upper-bound formula of the output vertex was given. The grids based on the output of experiment show that the spherical triangle generated by the grids of the proposed algorithm has no narrow angle, so it is suitable for calculating Ricci Flow.