Hyperspectral unmixing (HU) involves separating mixed pixel spectra into pure endmember spectra and their corresponding abundance fractions. However, it faces significant challenges due to outliers in the hyperspectral data, which often appear as pixel and band anomalies. Outliers in pixels could result in incorrect classification and inaccurate quantification of materials, while outliers in bands could alter spectral characteristics, leading to misidentifying endmembers and incorrect estimates of abundance. To tackle these issues, this paper introduces a new approach, named simultaneous outlier detection and elimination via weighted non-negative matrix tri-factorization (SODE-WNMTF), which offers an efficient means of addressing the impact of outliers in the unmixing process. Leveraging the co-clustering property of NMTF, SODE-WNMTF introduces a novel weighting matrix, which involves simultaneous clustering of both pixels and spectral bands to effectively detect and mitigate the negative impact of both pixel and band outliers during the unmixing process. At the same time, the inherent structure of the hyperspectral image (HSI) is utilized through the examination of local and global connections among pixels and spectral bands, consequently improving the co-clustering procedure. In addition, SODE-WNMTF proposes a spatial weighting factor, which utilizes the similarity of adjacent pixels, to promote piecewise smoothness in abundance maps while mitigating the impact of outliers. Moreover, since pixels in regions dominated by a single endmember exhibit spectra closely resembling that endmember, SODE-WNMTF incorporates a sparse estimation technique for endmember signatures. Finally, to verify the performance of SODE-WNMTF, a series of experiments is conducted on both synthetic and real HSIs, with outcomes proving its superiority against other cutting-edge approaches. The source code is also available at https://github.com/yasinhashemi/SODE-WNMTF. © The Author(s) 2025.