Under the condition of a low sampling rate, hyperspectral image (HSI) reconstruction faces important challenges in remote sensing. How to efficiently process HSI data is an urgent problem to be solved. We propose a hyperspectral image compressive sensing reconstruction (HSI-CSR) model based on tensor decomposition and a low-rank constraint. This model can efficiently exploit the underlying structure information in the HSI. Specifically, we study how to exploit reasonably the low-rank constraint of the core tensor and nonlocal self-similarity, respectively, to explore the nonlocal spatial–spectral similarity hidden in an HSI. To solve the proposed HSI-CSR model, we design an efficient algorithm based on the alternating direction method of multipliers knowledge. Finally, extensive simulations show that the proposed model achieves superior reconstruction performance, compared with other state-of-the-art methods.