Multi-user massive multiple-input multiple-output (MIMO) communication systems consume too much downlink bandwidth due to the huge channel state information (CSI) feedback, deep learning-based CSI feedback approaches fortunately can alleviate the feedback overhead while obtaining an accurate CSI. However, there is a trade-off between the high feedback performance and low computational complexity. In this paper, a low-complexity CSI feedback approach is proposed based on spatial and channel attention mechanism, namely the Spatial and Channel Attention Network (SCANet). Specifically, the spatial and channel attention mechanism makes the network’s attention mainly focus on the specific spatial regions and key feature channels. We devise a serial architecture in the encoder that composes of Spatial and Channel Attention Block (SCAB) and Encoder Transformer Block. Moreover, we design a hybrid architecture in the decoder that composes of the CNNs Block and Decoder Transformer Block. These designs enable the network to effectively extract both global and local CSI features. Computer simulations in both the indoor and outdoor scenarios show that under the same system configurations, the proposed low-complexity SCANet achieves almost the same performance as the state-of-the-art network while reducing the computational complexity by 85.76% fewer floating-point operations per second (FLOPS) on average.