Semantic segmentation is an important sub-task for many applications. However, pixel-level ground-truth labeling is costly, and there is a tendency to overfit to training data, thereby limiting the generalization ability. Unsupervised domain adaptation can potentially address these problems by allowing systems trained on labelled datasets from the source domain (including less expensive synthetic domain) to be adapted to a novel target domain. The conventional approach involves automatic extraction and alignment of the representations of source and target domains globally. One limitation of this approach is that it tends to neglect the differences between classes: representations of certain classes can be more easily extracted and aligned between the source and target domains than others, limiting the adaptation over all classes. Here, we address this problem by introducing a Class-Conditional Domain Adaptation (CCDA) method. This incorporates a class-conditional multi-scale discriminator and class-conditional losses for both segmentation and adaptation. Together, they measure the segmentation, shift the domain in a class-conditional manner, and equalize the loss over classes. Experimental results demonstrate that the performance of our CCDA method matches, and in some cases, surpasses that of state-of-the-art methods.