We developed the new crossover sine model (NSM) which is essential for thermodynamic calculations using the crossover equation of state. NSM was derived from trigonometric model [M.E. Fisher, S. Zinn and P.J. Upton, Phys. Rev. B 59, 14533 (1999)]– a kind of parametric models which are used to represent the thermodynamic variables near the critical point – as the crossover sine model (CSM) was developed. However, NSM is more theoretically strictly based on trigonometric model than CSM and thus we don't need to add any empirical expression to NSM. Also, by using NSM for thermodynamic calculations, we only need one additional crossover parameter besides original equation of state parameters. To test the performance of NSM, we applied the crossover lattice equation of state [M.S. Shin, Y. Lee and H. Kim, J. Chem. Thermodyn. 40, 174 (2008).] using the NSM(xLF/NSM) for correlations of various pure fluids and fluid mixtures. We showed that, over a wide range of states, the xLF/NSM yields the saturated properties of pure fluids and phase behaviours of binary mixtures than the original lattice equation of state. Moreover, the xLF/NSM presents good correlation results comparable with the crossover lattice equation of state / CSM using less system-dependent parameters.