In this work, a shim method that minimizes the maximum off-resonance frequency (min-max shim) in balanced steady-state free precession (bSSFP) is tested for brain imaging at 3T with constant and linear shim terms. The method demonstrates improvement of spatial coverage and banding artifact reduction over standard least-squares shimming. In addition, a new method (modified min-max shim) is introduced. This method reduces boundary band regions where the artifact is inevitable due to the excessive off-resonance frequency distribution. In comparison to standard least-squares shimming, the min-max based shim method either eliminates or reduces the size of banding artifacts. The method can be used to increase the signal-to-noise ratio (SNR) in bSSFP imaging or to increase the functional contrast in bSSFP functional MRI (fMRI) by allowing a longer usable repetition time (TR).