Recently, 3D medical image reconstruction (MIR) and segmentation (MIS) based on deep neural networks have been developed with promising results, and attention mechanism has been further designed for performance enhancement. However, the large size of 3D volume images poses a great computational challenge to traditional attention methods. In this paper, we propose a folded attention (FA) approach to improve the computational efficiency of traditional attention methods on 3D medical images. The main idea is that we apply tensor folding and unfolding operations to construct four small sub-affinity matrices to approximate the original affinity matrix. Through four consecutive sub-attention modules of FA, each element in the feature tensor can aggregate spatial-channel information from all other elements. Compared to traditional attention methods, with the moderate improvement of accuracy, FA can substantially reduce the computational complexity and GPU memory consumption. We demonstrate the superiority of our method on two challenging tasks for 3D MIR and MIS, which are quantitative susceptibility mapping and multiple sclerosis lesion segmentation.