The equilibrium compositions and thermodynamic properties(density,enthalpy,etc at constant pressure)of plasma of pure gases and mixtures under local thermodynamic nonequilibrium have been calculated in this paper.The homotopy Levenberg-Marquardt algorithm was proposed to accurately solve nonlinear equations with singular Jacobian matrices,and is constructed by the Saha equation and Guldberg-Waage equation combined with mass conservation,the electric neutrality principle and Dalton\'s partial pressure law,to solve the problem of dependence on the initial value in the process of iteration calculation.In this research,the equations at a higher temperature were solved and used as the auxiliary equations,and the homotopy control parameters\'sequence of the homotopy equations was selected by equal ratios.For auxiliary equations,the iterative initial value was obtained by assuming that there were only the highest-valence atomic cations and electrons at this temperature,and the plasma equilibrium composition distribution with the required accuracy was ultimately solved under the current conditions employing the Levenberg-Marquardt algorithm.The control parameter sequence was arranged according to the geometric sequence and the homotopy step was gradually shortened to ensure continuity of the homotopy process.Finally,the equilibrium composition and thermodynamic properties of pure N2,Mg(30％)-C02(70％)and Mg(40％)-CO(50％)-N2(10％)mixture plasma at atmospheric pressure were calculated and the calculation process of some specified temperatures was shown and analyzed.The calculation accuracy of equilibrium composition is higher than other findings in the literature.The results for the thermodynamic properties are in good agreement with data reported by the literature.