Spatial and spectral attention networks have been both well introduced to Hyperspectral image (HSI) classification. However, in previous works, they are seldom considered jointly. To obtain a 3D spatial-spectral attention map, which is beneficial for extracting discriminative spatial-spectral features, we propose a novel cooperative spatial-spectral attention network with tensor low-rank reconstruction. Firstly, a tensor low-rank reconstruction (TLRR) block is designed to learn a spatial-spectral attention map tensor, which adaptively emphasizes the attention features of the salient spatial positions and informative spectral bands simultaneously. Secondly, these attention features are merged into simple convolutional features which are more discriminative for classification. Finally, the experimental results demonstrate that our proposed method outperforms some state-of-the-art methods on two typical HSI datasets.