A ternary photonic crystal with left-handed material (LHM) layer is examined for refractometric applications. One of the layers is assumed to be air and treated as an analyte. The transmittance from the ternary photonic crystal is studied in details and the wavelength shift due to the change in the refractive index of the analyte is investigated. The transmittance is investigated with the parameters of the LHM. It is found that the wavelength shift can be significantly enhanced with the decrease of both real part of the LHM permittivity and thickness.