The applications of carbon dioxide in heat pump and refrigeration systems are based on a good understanding of its thermophysical properties. Equations of state (EoSs) are largely used to describe the thermophysical behaviors of fluids and can usually give satisfactory results at conditions far from the critical region. However, in the vicinity of the critical point, the long-wavelength of density fluctuations induce an asymptotic singular behavior of fluids, which cannot be described properly by the classical mean-field based EoS. The use of the renormalization group (RG) method with EoSs can correct this nonanalytical behavior near the critical point and not affect the classical behavior far away from the critical region. In this work, an RG method is applied to the Cubic-Plus-Association (CPA) EoS to build a crossover equation. A comprehensive study on thermophysical properties of carbon dioxide, containing vaporliquid phase equilibrium (VLE) of pure carbon dioxide and its binary mixtures with n-decane and water, compressed density, derivative properties, and transport properties, is performed using this crossover CPA (c-CPA) and the original CPA EoSs to analyze the effects of the RG method on these properties. Our results show that the RG approach can improve the EoSs performances on VLE, compressed density, and some derivative properties such as isobaric heat capacity, while there is no remarkable influence observed on the calculation of transport properties.