Compared to L2-norm based QSM reconstructions, methods based on L1-norm data consistency are less prone to artifact generation caused by phase inconsistencies (e.g. unwrapping artifacts, intravoxel dephasing). However, L2-norm methods present better denoising performance in high SNR regions. Here, we present a QSM algorithm that combines the strengths of the L1 and L2 norms, using Huber's loss function as the data consistency term. Simulations and in vivo reconstructions showed enhanced performance, with superior artifact suppression capabilities of our proposed method.