Semantic segmentation for remote sensing images (RSI) is critical for the Earth monitoring system. However, the covariate shift between RSI datasets under different capture conditions cannot be alleviated by directly using the unsupervised domain adaptation (UDA) method, which negatively affects the segmentation accuracy in RSI. We propose a stepwise domain adaptive segmentation network with covariate shift alleviation (Cov-DA) for RSI parsing to solve this issue. Specifically, to alleviate domain shift generated by different sensors, both the source and target domains are projected into a colorspace with normalized distribution through an elaborate colorspace mapping unified module (CMUM). The color distributions of these two domains tend to be more uniform. Furthermore, in the target domain, the multistatistics joint evaluation module (MJEM) is proposed to capture different statistical characteristics of subscenarios for selecting plain scenarios regarded as high-confidence segmentation results to assist the further improvement of segmentation performance. In addition, a pyramid perceptual attention module (PPAM) containing omnidirectional features without computational burdens is added to our network for effectively enhancing the multiscale feature capture ability. In the cross-city DA experiments based on the International Society for Photogrammetry and Remote Sensing (ISPRS) and aerial benchmarks, the superiority of our algorithm is significantly demonstrated. Furthermore, we release a large-scale Martian terrain dataset noted as "Mars-Seg" containing 5 K images with pixel-level accurate annotations regarding issues, such as the lack of semantic segmentation datasets for unknown scenes.