Deep learning achieves excellent performance in many domains, so we not only apply it to the navel orange semantic segmentation task to solve the two problems of distinguishing defect categories and identifying the stem end and blossom end, but also propose a fastidious attention mechanism to further improve model performance. This lightweight attention mechanism includes two learnable parameters, activations and thresholds, to capture long-range dependence. Specifically, the threshold picks out part of the spatial feature map and the activation excite this area. Based on activations and thresholds training from different types of feature maps, we design fastidious self-attention module (FSAM) and fastidious inter-attention module (FIAM). And then construct the Fastidious Attention Network (FANet), which uses U-Net as the backbone and embeds these two modules, to solve the problems with semantic segmentation for stem end, blossom end, flaw and ulcer. Compared with some state-of-the-art deep-learning-based networks under our navel orange dataset, experiments show that our network is the best performance with pixel accuracy 99.105%, mean accuracy 77.468%, mean IU 70.375% and frequency weighted IU 98.335%. And embedded modules show better discrimination of 5 categories including background, especially the IU of flaw is increased by 3.165%.