The damping constant for the tetragonal Raman peak at 308cm(-1) is calculated as a function of temperature close to the paraelectric-ferroelectric (T-C approximate to 400K) transition in BaTiO3. Expressions derived for the damping constant from the pseudospin-phonon coupled model and the energy fluctuation model are fitted to the experimental data for the bandwidths and integrated intensities of this Raman mode at various temperatures close to the paraelectric-ferroelectric transition in BaTiO3. The damping constant calculated from the pseudospin-phonon coupled model agrees well with the observed bandwidths of the tetragonal Raman mode studied in BaTiO3. The energy fluctuation model is not satisfactory to explain the observed behavior of the paraelectric-ferroelectric transition in BaTiO3. The experimental data from other sources also show similar critical behavior as our calculated values for the Raman bandwidths in BaTiO3. Our method of calculating the damping constant can be applied to some other ferroelectric crystals.