Semantic segmentation of remotely sensed images plays an important role in land resource management, yield estimation, and economic assessment. U-Net, a deep encoder-decoder architecture, has been used frequently for image segmentation with high accuracy. In this Letter, we incorporate multi-scale features generated by different layers of U-Net and design a multi-scale skip connected and asymmetric-convolution-based U-Net (MACU-Net), for segmentation using fine-resolution remotely sensed images. Our design has the following advantages: (1) The multi-scale skip connections combine and realign semantic features contained in both low-level and high-level feature maps; (2) the asymmetric convolution block strengthens the feature representation and feature extraction capability of a standard convolution layer. Experiments conducted on two remotely sensed datasets captured by different satellite sensors demonstrate that the proposed MACU-Net transcends the U-Net, U-NetPPL, U-Net 3+, amongst other benchmark approaches. Code is available at https://github.com/lironui/MACU-Net.