Dense 3D shape correspondence is an important problem in computer vision and computer graphics. Recently, the local shape descriptor based 3D shape correspondence approaches have been widely studied, where the local shape descriptor is a real-valued vector to characterize the geometrical structure of the shape. Different from these realvalued local shape descriptors, in this paper, we propose to learn a novel binary spectral shape descriptor with the deep neural network for 3D shape correspondence. The binary spectral shape descriptor can require less storage space and enable fast matching. First, based on the eigenvectors of the Laplace-Beltrami operator, we construct a neural network to form a nonlinear spectral representation to characterize the shape. Then, for the defined positive and negative points on the shapes, we train the constructed neural network by minimizing the errors between the outputs and their corresponding binary descriptors, minimizing the variations of the outputs of the positive points and maximizing the variations of the outputs of the negative points, simultaneously. Finally, we binarize the output of the neural network to form the binary spectral shape descriptor for shape correspondence. The proposed binary spectral shape descriptor is evaluated on the SCAPE and TOSCA 3D shape datasets for shape correspondence. The experimental results demonstrate the effectiveness of the proposed binary shape descriptor for the shape correspondence task.