Considerable numerical calculations are necessary to obtain equilibrium compositions for complex chemical systems. this requires a computer program to do the calculation and the numerical method for this program is described in detail. the complex chemical equilibrium compositions are calculated by a free-energy mininization technique. The program calculations of chemical equilibrium compostios are calculated by a free-energy mininization technique. The program calculations of chemical equilibrium compositions for assigned thermodynamic states such as （T,P） (H,P), (S,P), (T,V), (U,V), or (S,V), The program considers condensed species ans well as gaseous species and permits calculations of other thermodynamic properties (t,p,ρ,M,h,s,c_p, and so on) for any chemical system. These results can be applied to the fundamental design and analysis of analysis of equipment such as compressors, tirbines, nozzles, engines, shock tubes, heat exchangers, and chemical processing equipment.