Multi-object semantic segmentation from remote sensing images has gained significant attention in land resource surveying, global change monitoring, and disaster detection. Compared to other application scenarios, the objects in the remote sensing field are larger and have a wider range of distribution. In addition, some similar targets, such as roads and concrete-roofed buildings, are easily misjudged. However, existing convolutional neural networks operate only in the local receptive field, and this limits their capacity to represent the potential association between different objects and surrounding features. This paper develops a Multi-task Quadruple Attention Network (MQANet) to address the above-mentioned issues and increase segmentation accuracy. The MQANet contains four attention modules: position attention module (PAM), channel attention module (CAM), label attention module (LAM), and edge attention module (EAM). The quadruple attention modules obtain global features by expanding the receptive fields of the network and introducing spatial context information in the label. Then, a multi-tasking mechanism which splits a multi-category segmentation task into several binary-classification segmentation tasks is introduced to improve the ability to identify similar objects. The proposed MQANet network was applied to the Potsdam dataset, the Vaihingen dataset and self-annotated images from Chongzhou and Wuzhen (CZ-WZ), representative cities in China. Our MQANet performs better over the baseline net by a large margin of +6.33 OA and +7.05 Mean F1-score on the Vaihingen dataset, +3.57 OA and +2.83 Mean F1-score on the Potsdam dataset, and +3.88 OA and +8.65 Mean F1-score on the self-annotated dataset (CZ-WZ dataset). In addition, each image execution time of the MQANet model is reduced 66.6 ms compared to UNet. Moreover, the effectiveness of MQANet was also proven by comparative experiments with other studies.