Three processes of complex distillation are simulated using the Newton homotopy continuation method in this article. They are; (1) the dehydration of ethanol with benzene -five steady - state solutions under the same specifications from just one starting point; (2) three phase distillation for five components; (3) three phase reaction distillation for five components. The selection of the parameters for controlling the step size has been investigated under different cases for each problem. The facts of rapid convergence from any one starting point show that the algorithm is more robust. The results of simulations are in good agreement with the references and industrial experiments.