Monte Carlo (MC) simulation is carried out to study solidification of Si by a BCC lattice-gas model. To describe actual Si phases as quantitatively as possible, the Tersoff Si potential is mapped onto the BCC model by using the potential renormalization technique proposed by one of us. Using the renormalized potential, thermal properties are obtained for four plausible Si structures. The solidification process is studied by MC simulation. It is shown that calculation of the thermal properties of Si is greatly improved by using the lattice model with a renormalized potential.