Multi-objective optimization problems (MOOPs) with uncertainties are common in engineering design problems. To find the robust Pareto fronts, multi-objective robust optimization methods with inner-outer optimization structures generally have high computational complexity, which is always an important issue to address. Based on the general experience, robust Pareto solutions usually lie somewhere near the nominal Pareto points. Starting from the obtained nominal Pareto points, the search process for robust solutions could be more efficient. In this paper, we propose a method that sequentially approaching to the robust Pareto front (SARPF) from the nominal Pareto points. MOOPs are solved by the SARPF in two optimization stages. The deterministic optimization problem and the robustness metric optimization problem are solved in the first stage, and nominal Pareto solutions and the robust-most solutions can be found respectively. In the second stage, a new single-objective robust optimization problem is formulated to find the robust Pareto solutions starting from the nominal Pareto points in the region between the nominal Pareto front and the robust-most points. The proposed SARPF method can save a significant amount of computation time since the optimization process can be performed in parallel at each stage. Vertex estimation is also applied to approximate the worst-case uncertain parameter values which can save computational efforts further. The global solvers, NSGA-II for the multi-objective case and genetic algorithm (GA) for the single-objective case, are used in corresponding optimization processes. Two examples with comparison to a previous method are presented for the applicability and efficiency demonstration.