Affected by the angle of illumination, the images of small bodies taken by the spacecraft are incomplete, and it is difficult to reconstruct them with existing algorithms. To solve this problem, a 3D reconstruction algorithm for small bodies based on incomplete contours was proposed. Firstly, the image was subjected to threshold segmentation using the Otsu algorithm, and the extraction of incomplete contours was performed using the EDPF (edge drawing parameter free) algorithm. Subsequently, leveraging the solar azimuth information and combining it with the incomplete contours, the influence of shadows was taken into account. This process involved retaining both the illuminated regions and potential areas, resulting in the computation of expanded contours. Next, through the utilization of a set of expanded contours and projection matrices, the computation of the 3D bounding box was transformed into a linear inequality problem. Finally, voxel partitioning was performed to accomplish the 3D reconstruction of the small body. The quality of reconstruction was evaluated by normalizing the Hausdorff distance between the reconstructed results and reference models using the average radius. The simulation results indicate that the distribution probability of reconstruction errors being less than 4% is over 95%, and the algorithm also shows a certain level of robustness against changes in the angle of illumination.