The design and management of chemical manufacturing process, including performance assessment and product quality evaluation, alway involve frequent simulation, The equation-oriented approach is one of the most competitive strategies in process simulation, but this approach is difficult to implement because of the complexity and nonlinearity of chemical processes. In this study, a homotopy-based backtracking method (HBM) for simulation is improved with a second order correction, which can be calculated with low computational cost. The theoretical foundation for the proposed homotopy with second-order correction based backtracking method (SOC-HBM) is also established. simulation runs of production of secreted protein in fed-batch reactor, a penicillin termentation process, and a binary distillation column system are demonstrated using SOC-HBM