In this work, an improved Hulburt–Hirschfelder (IHH) potential energy function (PEF) has been constructed with an extra adjustable parameter. Applying the determined IHH potential points to the one-dimension Schrödinger equation can yield the exact solution viz. the rovibrational energies, which are used for the calculations of internal partition function, molar heat capacity, Gibbs-free energy, entropy and enthalpy within the framework of the quantum statistical ensemble theory. Comprehensive comparisons for the ground electronic state of carbon monoxide show that the IHH potentials can get good approach in the asymptotic and the dissociation regions, and these thermodynamic properties (TP) determined by IHH model are supported by the good agreement with experimental data in a temperature range of T ≤ 6000 K. [ABSTRACT FROM AUTHOR]