The Lee-Kesler equation can accurately describe the P-V-T properties of multi-component hydrocarbon mixtures, which is usually used to calculate the state of equation of the heavy oil during simulating the chemical compound flooding process. By incorporating the advantages of Newton and bisection methods, a hybrid Newton-Bisection algorithm based on the minimum free energy principle is proposed for solving the Lee-Kesler equation. This algorithm follows the idea of bisection method at the beginning to quickly find the target interval from the definition domain of Lee-Kesler equation. After that, the Newton iterative formula is used to calculate the real root in the interval and the corresponding Gibbs free energy. Finally, the process is iterated until the free energy no longer decreases. There are three advantages of the hybrid Newton-Bisection algorithm. First of all, it is robust and insensitive to the initial value. Secondly, the calculation can be converged quickly, which is 1-2 times faster than the bisection method. Moreover, it has a wide range of applications and can be applied to calculate the P-V-T properties of both gas and liquid mixtures. Compared with the Newton and bisection methods, the hybrid Newton-Bisection algorithm is more suitable to be embedded in simulation software to calculate the P-V-T properties of the hydrocarbon mixtures.