A multi-objective structural optimization method based on parametric cross-section modeling was investigated to enable the direct optimization of structural dimensions for variable cross-section links in lightweight collaborative robot design. First, the mapping between multiple dimensional parameters of variable cross-section links and their stiffness matrices was established based on the Euler-Bernoulli beam model. Combined with the finite element method, a static stiffness model and a natural frequency model for arbitrary postures of the entire robot were constructed and solved in real time. Subsequently, the cross-sectional dimensional parameters were selected as optimization variables. A multi-objective optimization model was formulated with the objectives of maximizing the natural frequency, minimizing the mass, and minimizing the static deformation. With several working-condition poses as reference points, the multi-objective optimization problem was solved using the NSGA-Ⅱ(non-dominated sorting genetic algorithm Ⅱ). The results show that the robot mass is reduced by 1.06 kg while the static deformation is decreased. Meanwhile, the first-order natural frequencies at five different postures are increased by 7.39% to 11.62%. The effectiveness of the proposed method is thus fully verified. The multi-objective structural optimization method based on parametric section modeling proposed can effectively realize the coordinated improvement of lightweight and dynamic-static performance of the variable-section arm of collaborative robots, and provides an efficient and feasible technical path for the optimal design of the arm structure of collaborative robots.