An influence of the localization of itinerant electrons induced by correlated hopping on the electronic charge and heat transport is discussed for the lightly doped Mott insulator phase of the Falicov-Kimball model. The case of strongly reduced hopping amplitude between the sites with occupied f -electron levels, when an additional band of localized d-electron states could appear on the DOS in the Mott gap, is considered. Due to the electron-hole asymmetry and anomalous features on the DOS and transport function induced by correlated hopping, a strong enhancement of the Seebeck coefficient is observed at low temperatures, when the flattened dependence is displayed in a wide temperature range.which introduces new physical effects because now the value of inter-site hopping depends on the occupation of these states.Local Coulomb interaction is a subject of the famous Hubbard model and has been investigated for many decades in the theory of strongly correlated electron systems, whereas the correlated hopping attracts much less attention. Mainly, it was considered in connection with the elaboration of new mechanisms for high temperature superconductivity [3,4], description of organic compounds [5] and molecular crystals [6], electron-hole asymmetry [7], and enhancement of magnetic properties [8]. The recent years show that correlated hopping is an important puzzle in the physics of quantum dots [9-11] and it appears in a natural way in modelling the fermionic [12,13] and bosonic [14-16] atoms on optical lattices.