In present work, an improved regular solution model is established, based on the concept of regular solution and local composition theory. The local volume fractions phi(ij) are considered to include the influence of interaction energy between molecules on molecules' local distribution. A new expression for molar excess Gibbs free energy (g(E)) is developed for the calculation of activity coefficients. Regular solution (RS), Wilson (W) and modified regular solution (MRS) are used for the non-ideality of solid phase and regular solution is adopted for liquid phase. Compared with the experimental data of binary, ternary and quaternary n-allcane systems, the advantage of RS-MRS is illustrated, with the best predictions of wax appearance temperature (WAT) and solid precipitation curve, which proves that the non-random molecules distribution caused by interaction energy between molecules is essential for g(E). It is the application phi(ij) that enhances the prediction accuracy of RS-MRS. (C) 2016 Elsevier B.V. All rights reserved.