An enhanced simulated annealing algorithm (SAA) is presented to verify the phase stability analysis and obtain the true solution of the phase equilibrium problem of multi-component systems at high pressures. Using the enhanced SAA, the global stability analysis is checked on the basis of the minimization results of the tangent plane distance functions (TPDF) for the systems where the nonideal phases are described by PR or SRM equations of state. The consequent phase equilibrium calculation is accomplished by the Newton-Raphson method based upon the stability analysis results. The calculation results for three systems including ternary, quaternary, and five-component mixtures that exhibit multiple immiscibility gaps with different charges at elevated pressures state that the combined algorithm can effectively locate the global minima of these systems involving symmetric models, then the final stability analysis implemented is used to ensure the global minimization. In comparison with MULPRG and HOMPEQ developed by Michelsen and Sun and Seider (1995: Fluid phase Equilibrium, 103, 213-249) respectively, the enhanced SAA is slightly slower and provides comparable reliability, but it is self-starting.