The convergence of the rate model of multi-component non-linear liquid chromatography is studied in detail. The key step of solving this model is to select the appropriate interpolation method, which determines the rapidity of convergence of the model. Two interpolation methods, the linear interpolation method and the three-point Lagrange interpolation method, are compared in calculating the model. The results show that when the Lagrange interpolation is used the efficiency of calculation is elevated significantly. The calculation converges quickly at low finite element number.