The damping constant (linewidth) of the LA mode is calculated as a function of temperature for the incommensurate (INC) phase of quartz by using the models of the pseudospin-phonon (PS) coupled and the energy fluctuation (EF). For this calculation, the observed linewidth (Gamma(LA)) data are used at P = 0 and 80.5MPa from the literature. Close to the incommensurate phase between the alpha and beta phases of quartz, the observed Gamma(LA) and the frequency shifts (Delta v(LA) ) are also analyzed by the power-law formula for both pressures (P = 0 and 80.5MPa). By using the Gamma(LA) and Delta v(LA), the inverse relaxation time (tau(-1)(LA)) is predicted as a function of temperature (P = 0 and 80.5MPa) in the incommensurate phase of quartz and the values of the activation energy (E-a) are deduced. Our calculated Gamma(LA) from both models (PS and EF) explain adequately the observed behavior of the linewidth of the LA mode in the incommensurate phase of quartz. Also, our predicted tau(-1)(LA) can be compared with the measurements in the INC phase of this molecular crystal.