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Extracting roads from high-resolution remote sensing images (HRSIs) is vital in a wide variety of applications, such as autonomous driving, path planning, and road navigation. Due to the long and thin shape as well as the shades induced by vegetation and buildings, small-sized roads are more difficult to discern. In order to improve the reliability and accuracy of small-sized road extraction when roads of multiple sizes coexist in an HRSI, an enhanced deep neural network model termed Dual-Decoder-U-Net (DDU-Net) is proposed in this paper. Motivated by the U-Net model, a small decoder is added to form a dual-decoder structure for more detailed features. In addition, we introduce the dilated convolution attention module (DCAM) between the encoder and decoders to increase the receptive field as well as to distill multi-scale features through cascading dilated convolution and global average pooling. The convolutional block attention module (CBAM) is also embedded in the parallel dilated convolution and pooling branches to capture more attention-aware features. Extensive experiments are conducted on the Massachusetts Roads dataset with experimental results showing that the proposed model outperforms the state-of-the-art DenseUNet, DeepLabv3+ and D-LinkNet by 6.5%, 3.3%, and 2.1% in the mean Intersection over Union (mIoU), and by 4%, 4.8%, and 3.1% in the F1 score, respectively. Both ablation and heatmap analyses are presented to validate the effectiveness of the proposed model.