In order to improve the load-bearing capacity and dynamic stability of C-type frame for riveting equipment, its structure was optimized based on the shape optimization theory and finite element method. According to the riveting process requirements, the finite element model of C-type frame was established, and the maximum working load was set to be 70 kN, which was suitable for riveting scenarios where the combined thickness of plates ranged from 1.5 mm to 6.0 mm. Then, through the static analysis, it was found that the stress distribution of the original frame was uniform under the limit load, but the strength of the local area was insufficient, and the maximum deformation displacement reached 1.985 mm. The modal analysis shows that the 1st-order and 2nd-order natural frequencies of model a were 132.26 and 133.57 Hz, respectively, and there was a risk of resonance. Furthermore, aiming at the above problems, a comprehensive optimization strategy with the objectives of improving the stiffness and suppressing the deformation was proposed, which integrated topology optimization and parametrized level set method, reconstructed the material distribution and adjusted the frame geometry state. After the optimization, the safety coefficient of C-type frame was increased to 1.74, the maximum deformation displacement was reduced to 0.605 mm, and the fundamental frequency was increased to 222.12 Hz, which effectively avoided resonance and improved the dynamic response. The results show that the optimized design significantly improves the mechanical properties and stability of the frame under the constraint of lightweight, which provides theoretical support for the efficient design and engineering application of riveting equipment.