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Cloud segmentation is a fundamental step in accurately acquiring cloud cover. However, due to the nonrigid structures of clouds, traditional cloud segmentation methods perform worse than expected. In this paper, a novel deep convolutional neural network (CNN) named MA-SegCloud is proposed for segmenting cloud images based on a multibranch asymmetric convolution module (MACM) and an attention mechanism. The MACM is composed of asymmetric convolution, depth-separable convolution, and a squeeze-and-excitation module (SEM). The MACM not only enables the network to capture more contextual information in a larger area but can also adaptively adjust the feature channel weights. The attention mechanisms SEM and convolutional block attention module (CBAM) in the network can strengthen useful features for cloud image segmentation. As a result, MA-SegCloud achieves a 96.9% accuracy, 97.0% precision, 97.0% recall, 97.0% F-score, 3.1% error rate, and 94.0% mean intersection-over-union (MIoU) on the Singapore Whole-sky Nychthemeron Image Segmentation (SWINySEG) dataset. Extensive evaluations demonstrate that MA-SegCloud performs favorably against state-of-the-art cloud image segmentation methods.