Binocular stereo vision is a common way for 3D reconstruction of objects, which is core technology in the fields of computer-aided geometric design, machine vision and so on. However, the conventional binocular stereo vision algorithms are very sensitive to the ambient lighting, restricting their further promotion. The method of tensor completion, applied to the progress of preprocessing the captured binocular image, provides a way to solve this problem. In this paper, a binocular stereo vision algorithm that uses low-rank tensor completion to perform 3D reconstruction is presented. In the pictures, the positions where the ambient illumination are strong are regarded as information that cannot be observed, and the others are regarded as observable information. The unobservable information will be completed using the observable information based on tensor completion. The results show that the 3D reconstruction results obtained using tensor completion are better than those without tensor completion.