We propose a two-stage QSM method, Quantitative Susceptibility Mapping Artifact Reduction Technique (QSMART), in which tissue and vein susceptibility values are estimated in parallel by generating a vasculature mask from the magnitude data using a Frangi filter. Spatially Dependent Filtering is employed for the background field removal and the two susceptibility estimates are combined in the final QSM map. QSMART is compared to RESHARP/iLSQR and V-SHARP/iLSQR inversion on 7T in vivo single and multiple-orientation scans. QSMART demonstrates superior artifact suppression in the cortex and near vasculature, and is a robust tool for susceptibility estimation. QSMART code is available at https://github.com/MBCIU/QSMART.