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Two different potential models to the molecular dynamics (MD) simulations have been applied to investigate the thermoelastic parameter alpha K-T of sodium chloride (NaCl) under high pressure and high temperature. The first one is the shell model (SM) potential that due to the short-range interaction when pairs of ions are moved together as is the case in that polarization of a crystal due to the motion of the positive and negative ions, and the second one is the two-body rigid-ion Born-Mayer-Huggins-Fumi-Tosi (BMHFT) potential with full treatment of long-range Coulomb forces. Particular attention is paid to the comparison of the SM- and BMHFT-MD simulations with the Debye model for the first time, and this model combines with ab initio calculations within local density approximation (LDA) and generalized gradient approximation (GGA) using ultrasoft pseudopotentials and a plane-wave basis in the framework of density functional theory (DFT), and it takes into account the phononic effects within the quasi-harmonic approximation. Note that the MD calculated volumes using SM model is somewhat larger than both the DFT and experimental volumes despite not considering the temperature effect. Compared with SM potential, the MD simulated 300 K isotherm of NaCl with BMHFT potential is very successful in reproducing accurately the measured volumes and the GGA calculated volumes. Generally, it is found that there exist minor differences between the LDA and GGA computed the thermoelastic parameter alpha K-T of NaCI, with both average results giving good agreement with SM-MD simulations. At an extended pressure and temperature ranges, the variation of thermoelastic parameter alpha K-T which play a central role in the formulation of approximate equations of state has also been predicted. The properties of NaCl are summarized in the pressure range of 0-300 kbar and the temperature up to 2000 K. (C) 2012 Elsevier Ltd. All rights reserved.