Free-space optical communication brings large-capacity communication with excellent confidentiality, though fatal obstacles are set by atmospheric turbulence that causes phase shifting in laser links. Therefore, we derived a novel, to the best of our knowledge, iterative wavefront correction algorithm based on a complete second-order deformable mirror (DM) Shack-Hartmann wavefront sensor model as a solution to it. For correcting static wavefront aberration, the proposed algorithm possesses a converging speed faster than the traditional one. In terms of correcting dynamic atmospheric turbulence, it can achieve convergence within two iterations with a residual wavefront root mean square value of less than 1/8 wavelength. The input wavefront under 1.5 wavelength can be corrected on our testbed due to the deformability of the micromachined membrane DM. The research result offers a solution for atmospheric turbulence in the adaptive optics field and may contribute to the development of free-space optical communication.