A new generalized algorithm for chemical equilibrium calculation is presented. This method can effectively determine whether a pure solid phase exists and accurately evaluate the compositions of trace species with the extents of reaction and moles of components as the iterative variables. The efforts required for the inverse of Jacobian matrix are equivalent to the method where only the extents of reaction are iterative variables by a linear transformation. This approach begins with estimating the initial value with relaxation method and convergence can be accelerated by Newton-Raphson method. The singularity of Jacobian matrix can be overcome with the help ot damped Newton-Raphson method. The approach has the same robustness as Marquardt method used by Xiao et al. (1989). All the examples tested converge to the correct solutions from zero iterative variables. The carbonation of methane steam shift system and the chemical vapor deposition of Ti(C

N) are analy-sized. The computed results of NH3-CO2-SO2-H2S-CH4-C2H6 system are also presented.