The results of calculations of coil magnetization effect in the Nb₃Sn high field magnet being developed at Fermilab for VLHC and different possibilities of its correction using simple and inexpensive iron shims will be presented. Using the proposed correction techniques, the injection field in this magnet could be reduced to 0.5-1 T, which significantly increases the magnet operation field range. The requirements to the effective filament size in the Nb₃Sn strands will be also discussed.