The reflective spectrums of the cholesteric liquid crystals under the condition of normal incident light are computed by using Jones matrix method. A theoretical model for discussing the influence of the transverse electric field on the twist angle and the pitch of the planar texture cholesteric liquid crystals under the in-plane switching mode is established. Based on the model, the relation between the electric field and the reflective peak for the cholesteric liquid crystals, and the relation between the electric field and the reflective spectral width for the cholesteric liquid crystals are calculated. The effects of the transverse electric field on the pitch and the reflective characteristics of the planar texture cholesteric liquid crystals are studied under different anchoring conditions. The results show that, under the in-plane switching mode, the color of the light reflected from the cholesteric liquid crystals can be changed by the applied transverse electric field, which supplies a theoretical support for the planar texture cholesteric LC color display based on the electrically-controlled pitch.