We experimentally observed that the photonic band gap (reflection band) of polymer stabilized cholesteric liquid crystals with negative dielectric anisotropies can be greatly broadened under DC electric fields. We explored the underlying mechanism. We found that the dispersed polymer network moved when DC voltages were applied across the liquid crystal cell. The motion of the polymer network stretched the helical pitch of the liquid crystal on one side of the cell and compressed the helical pitch on the other side of the cell. We proposed a phenomenological theory to explain the motion of the polymer network and the effect of the polymer network on the helical pitch, and this theoretical prediction agreed well with the experimental results.