Hyperspectral　images　(HSIs)　contain　rich　spatial　and　spectral　information.　A　double　dispersers　coded　aperture　snapshot　spectral　imaging　(DD-CASSI)　system　takes　advantage　of　compressive　sensing　(CS)　theory　to　map　3-D　HSI　data　into　a　single　2-D　measurement.　One　of　the　key　components　of　DD-CASSI　is　to　reconstruct　high-quality　HSI　from　measurement.　Traditional　model-based　methods　use　mathematical　optimization　to　reconstruct　HSIs　according　to　prior　knowledge.　Current　deep　learning-based　methods　achieve　pleasant　results.　However,　fully　learned　deep　learning　methods　lack　interpretability,　and　model-based　deep　learning　methods　cannot　achieve　pleasant　performance.　In　this　article,　we　propose　a　novel　HSI　reconstruction　framework　na　med　refinement　boosted　and　attention　guided　tensor　fast　iterative　shrinkage-thresholding　algorithm-Net　(ReAttFISTA-Net),　which　combines　model-based　deep　learning　and　fully　learned　deep　learning　reconstruction　strategies.　In　this　framework,　we　introduce　an　attention　guided　fusion　mechanism,　which　enhances　spatial-spectral　information,　refinement　subnetwork,　and　auxiliary　loss　terms　to　improve　the　reconstruction　performance.　Extensive　experimental　results　show　that　the　proposed　reconstruction　algorithm　outperforms　the　state-of-the-art　algorithms　on　both　simulation　and　real-world　datasets.