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The snapshot hyperspectral imaging is an emerging technique with numerous applications. However, the hyperspectral imaging reconstruction is often time-consuming, which is placing a limit on the development of snapshot hyperspectral imaging. We present an efficient reconstruction algorithm based on the tensor analysis and the low-rank constraint. The hyperspectral data cube is regarded as a low rank three-order tensor, which can jointly treat both spatial and spectral modes. The 3D-LRC method can greatly decrease the computation time without unfolding the hyperspectral data cube into 2D patches. Compared with the-state-of-the-art method, the proposed method has a great improvement in the reconstruction speed and quality. The method has been implemented on two typical snapshot hyperspectral imaging systems.