In this article, based on finite element discretization, we propose one- and two-level Arrow–Hurwicz-type iterative algorithms for solving the steady-state Smagorinsky equations. The two-level Arrow–Hurwicz-type iterative algorithm involves solving a linearization Smagorinsky problem by the Arrow–Hurwicz-type iteration on a coarse mesh with mesh size H, and one Oseen-type linear problem on a fine mesh with mesh size h. Stability analysis and error estimation are provided. Compared with the classical Arrow–Hurwicz algorithm, the proposed algorithms have less constriction concerning parameter. Finally, we test some numerical experiments to illustrate the effectiveness of the proposed algorithms.