Hyperspectral unmixing aims to identify the spectral characteristics of substances (endmembers) and spatial distribution (abundance) features of substances (end-elements) from a blind source separation scenario. To address the challenges posed by a large number of mixed pixels in hyperspectral images, which can reduce unmixing accuracy, and the difficulty in accurately estimating the number of endmembers when hyperspectral data is contaminated with noise, a hyperspectral unmixing model that combines low-rank relaxation and separable total variation prior information is proposed in this paper. Firstly, the local similarity of the logarithmic function is utilized to relax the nuclear norm-based low-rank expression, thereby suppressing minor components. Then, the anisotropic total variation is redefined as a separable expression to smooth the spectral characteristics and spatial abundance features. Finally, a set of efficient solvers is designed to obtain a closed-form solution. The experimental results show that the proposed unmixing model can effectively improve the unmixing accuracy while suppressing the noise, which verifies the effectiveness of the model.