The thermodynamics of a complex solution system, Cu(Ⅱ)-NH_3-NH_4Cl-H_2O, was presented both theoretically and experimentally. Firstly, according to the principles of simultaneous equilibrium and aqueous electronic charge neutrality of the system, a nonlinear mathematical thermodynamic model with multi-members was set up. In this model, there were six unknowns: pH value, concentration values of free Cl~-, free NH_3, total concentration values of Cu~(2+), Cl~- and NH_3, four equilibrium equations and three equilibrium equations of total quantum of Cu~(2+), Cl~- and NH_3, as well as an equilibrium equation of electric charge, were involved in the model. Then after specifying the values of total concentrate of NH_3 and Cl~-, the model was solved precisely using MATLAB language, and the other four unknowns were obtained. According to the values obtained above, various valuable figures regarding thermodynamic relation of the system were protracted also with MATLAB, including two and three dimensions figures. These figures and data can supply the theoretic conference for optimizing the ratio of leaching reagents in copper extraction through ammonia hydrometallurgy. Finally, the solubility of CuO were measured in the system of NH_3-NH_4Cl-H_2O. The results show that the model and the thermodynamic data obtained are reliable. The thermodynamics of a complex solution system, Cu (II) -NH_3-NH_4Cl-H20, was presented both theoretically and experimentally. Firstly, according to the principles of simultaneous equilibrium and aqueous electronic charge neutrality of the system, a nonlinear mathematical thermodynamic model with multi-members was set up. In this model, there were six unknowns: pH value, concentration values ​​of free Cl ~ -, free NH_3, total concentration values ​​of Cu ~ (2+), Cl ~ - and NH_3, four equilibrium equations and three equilibrium equations of total quantum of Cu ~ (2+), Cl ~ - and NH_3, as well as an equilibrium equation of electric charge, were involved in the model. Then after specifying the values ​​of total concentrate of NH_3 and Cl ~ -, the model was solved precisely using MATLAB language, and the other four unknowns were obtained. According to the value obtained above, various valuable figures regarding thermodynamic relation of the system were protracted also with MATLAB, including two and three dimensions figures. These figures and data can supply the theoretic conference for optimizing the ratio of leaching reagents in copper extraction through ammonia hydrometallurgy. Finally, the solubility of CuO were measured in the system of NH_3-NH_4Cl-H_2O. The results show that the model and the thermodynamic data obtained are reliable.