We propose FaceCom, a method for 3D facial shape completion, which delivers high-fidelity results for incomplete facial inputs of arbitrary forms. Unlike end-to-end shape completion methods based on point clouds or voxels, our approach relies on a mesh-based generative network that is easy to optimize, enabling it to handle shape completion for irregular facial scans. We first train a shape generator on a mixed 3D facial dataset containing 2405 identities. Based on the incomplete facial input, we fit complete faces using an optimization approach under image inpainting guidance. The completion results are refined through a post-processing step. FaceCom demonstrates the ability to effectively and naturally complete facial scan data with varying missing regions and degrees of missing areas. Our method can be used in medical prosthetic fabrication and the registration of deficient scanning data. Our experimental results demonstrate that FaceCom achieves exceptional performance in fitting and shape completion tasks.