This abstract presents a fast nonlinear solver for the QSM reconstruction using the total generalized variation regularization. The proposed method utilizes the alternating direction method of multipliers to obtain close-form solution to each sub-problem. To handle the non-linear data fidelity, a two-step algorithm is described, including a global optimum search and a local Newton-Raphson iteration. Compared to conventional linear solvers, nonlinear solutions reduce streaking artifacts and better handle noise in poor SNR regions. Reconstruction results are at least comparable to nonlinear MEDI in quality, but with an order of magnitude improvement in the computational efficiency.