The authors model a cholesteric liquid crystal material in which periodic elongation or shortening of the pitch has been introduced, and investigate its optical properties by the plane wave expansion method. The calculated photonic band structure revealed a continuous shift of the selective reflection band depending on the sign and degree of the modulation in pitch introduced. Anomalous selective reflection band-gaps were also observed at frequencies higher and lower than the original band-gap of the unmodified cholesteric liquid crystal, due to the longer periodicity experienced by the light interacting with the material.