Integrating spatial information into the sparse subspace clustering (SSC) models for hyperspectral images (HSIs) is an effective way to improve clustering accuracy. Since HSI is a three-dimensional (3D) cube datum, 3D spectral-spatial filtering becomes a simple method for extracting the spectral-spatial information. In this paper, a novel spectral-spatial SSC framework based on 3D edge-preserving filtering (EPF) is proposed to improve the clustering accuracy of HSI. First, the initial sparse coefficient matrix is obtained in the sparse representation process of the classical SSC model. Then, a 3D EPF is conducted on the initial sparse coefficient matrix to obtain a more accurate coefficient matrix by solving an optimization problem based on ADMM, which is used to build the similarity graph. Finally, the clustering result of HSI data is achieved by applying the spectral clustering algorithm to the similarity graph. Specifically, the filtered matrix can not only capture the spectral-spatial information but the intensity differences. The experimental results on three real-world HSI datasets demonstrated that the potential of including the proposed 3D EPF into the SSC framework can improve the clustering accuracy.