As additive manufacturing advances, it offers a cost-effective avenue for structurally repairing components. However, a challenge arises in the additive repair of suspended damaged surfaces, primarily due to gravitational forces. This can result in excessive deformation during the repair process, rendering the formation of proper repair impractical and leading to potential failure. In light of this rationale, conventional repair techniques are impractical for extensively damaged surfaces. Thus, this article proposes a novel repair methodology that is tailored to address large-area damage. Moreover, and departing from conventional practices involving the addition and subsequent subtraction of materials for precision machining, the proposed process endeavors to achieve more precise repair outcomes in a single operation. This paper introduces an innovative repair approach employing fused deposition modeling (FDM) to address the complexities associated with the repair of damaged polymer material parts. To mitigate geometric errors in the repaired structural components, beams with minimal deformation are printed using a compensation method. These beams then serve as supports for overlay printing. The paper outlines a methodology by which to determine the distribution of these supporting beams based on the shape of the damaged surface. A beam deformation model is established, and the printing trajectory of the compensated beam is calculated according to this model. Using the deformation model, the calculated deformation trajectories exhibit excellent fitting with the experimentally collected data, with an average difference between the two of less than 0.3 mm, validating the accuracy of the suspended beam deformation model. Based on the statistical findings, the maximum average deformation of the uncompensated sample is approximately 5.20 mm, whereas the maximum deformation of the sampled point after compensation measures around 0.15 mm. Consequently, the maximum deformation of the printed sample post-compensation is mitigated to roughly 3% of its pre-compensation magnitude. The proposed method in this paper was applied to the repair experiment of damaged curved surface components. A comparison was made between the point cloud data of the repaired surface and the ideal model of the component, with the average distance between them serving as the repair error metric. The mean distance between the point clouds of the repaired parts using the proposed repair strategy is 0.197 mm and the intact model surface is noticeably less than the mean distance corresponding to direct repair, at 0.830 mm. The repair error with compensatory support beams was found to be 76% lower than that without compensatory support beams. The surface without compensatory support beams exhibited gaps, while the surface with compensatory support beams appeared dense and complete. Experimental results demonstrate the effectiveness of the proposed method in significantly reducing the geometric errors in the repaired structural parts. The outcomes of the FDM repair method are validated through these experiments, affirming its practical efficacy. It is noteworthy that, although only PLA material was used in this study, the proposed method is general and effective for other polymer materials. This holds the potential to significantly reduce costs for the remanufacturing of widely used polymers.