Purpose To develop a tissue field‐filtering algorithm, called maximum spherical mean value (mSMV), for reducing shadow artifacts in QSM of the brain without requiring brain‐tissue erosion. Theory and Methods Residual background field is a major source of shadow artifacts in QSM. The mSMV algorithm filters large field‐magnitude values near the border, where the maximum value of the harmonic background field is located. The effectiveness of mSMV for artifact removal was evaluated by comparing existing QSM algorithms in numerical brain simulation as well as using in vivo human data acquired from 11 healthy volunteers and 93 patients. Results Numerical simulation showed that mSMV reduces shadow artifacts and improves QSM accuracy. Better shadow reduction, as demonstrated by lower QSM variation in the gray matter and higher QSM image quality score, was also observed in healthy subjects and in patients with hemorrhages, stroke, and multiple sclerosis. Conclusion The mSMV algorithm allows QSM maps that are substantially equivalent to those obtained using SMV‐filtered dipole inversion without eroding the volume of interest.