We report an optical spectroscopy study on the newly discovered superconductor Cu0.07TiSe2. Consistent with the development from a semimetal or semiconductor with a very small indirect energy gap upon doping TiSe2, it is found that the compound has a low carrier density. Most remarkably, the study reveals a substantial shift of the screened plasma edge in reflectance towards high energy with decreasing temperature. This phenomenon, rarely seen in metals, indicates either a sizable increase of the conducting carrier concentration or/and a decrease of the effective mass of carriers with reducing temperature. We attribute the shift primarily to the latter effect.