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Whereas the transform coding algorithms have been proved to be efficient and practical for grey-level and color images compression, they could not directly deal with the hyperspectral images (HSI) by simultaneously considering both the spatial and spectral domains of the data cube. The aim of this paper is to present an HSI compression and reconstruction method based on the multi-dimensional or tensor data processing approach. By representing the observed hyperspectral image cube to a 3-order-tensor, we introduce a tensor decomposition technology to approximately decompose the original tensor data into a core tensor multiplied by a factor matrix along each mode. Thus, the HSI is compressed to the core tensor and could be reconstructed by the multi-linear projection via the factor matrices. Experimental results on particular applications of hyperspectral remote sensing images such as unmixing and detection suggest that the reconstructed data by the proposed approach significantly preserves the HSI׳s data quality in several aspects.