A novel quantum optimization algorithm has been developed, enabling the approximation of ground states for classical Ising Hamiltonians through a self-consistent mean-field approach. By decomposing complex problems into independent subproblems, the algorithm treats interactions between them in a mean-field manner, leveraging a common environment constructed via a variational quantum circuit. This environment is refined self-consistently, allowing for more accurate approximations. The introduction of this algorithm has significant implications for optimization problems, particularly those with complex interaction terms1. As quantum computing continues to advance, such algorithms will play a crucial role in tackling challenging problems in fields like materials science and logistics. The development of this algorithm matters to practitioners because it has the potential to unlock more efficient solutions to complex optimization problems, which could, in turn, drive breakthroughs in various fields.