An iteration-variable-correction (IVC) based method is proposed for solving optimal power flow (OPF) of transmission-distribution-coupled (TDC) systems. First, a TDC system can be divided into a single coordinator and multiple agents. Then, the basic formulation, subproblem construction, and selection of iteration variables are given based on the conventional heterogeneous decomposition algorithm (HGD). Considering the limitations of the conventional HGD, the IVC is proposed. According to the general theory of the IVC, when it is applied to solve TDC OPF, the voltage magnitude of boundary buses and the multipliers corresponding to boundary power injections will be corrected every four iterations with first-order and second-order differential operations on historical results in the previous four iterations. The quadratic convergence of the IVC is proved under several weak assumptions. The numerical experiments demonstrate that the proposed IVC has the same accuracy as the method based on the centralized OPF model. Also, better convergence and efficiency can be achieved under the IVC compared with some conventional decomposition methods, including alternating direction method of multipliers, auxiliary problem principle method, analytical target cascading method, and the HGD.