Covid-19 has swept the world since 2020, taking millions of lives. In order to seek a rapid diagnosis of Covid-19, deep learning-based Covid-19 classification methods have been extensively developed. However, deep learning relies on many samples with high-quality labels, which is expensive. To this end, we propose a novel unsupervised domain adaptation method to process many different but related Covid-19 X-ray images. Unlike existing unsupervised domain adaptation methods that cannot handle conditional class distributions, we adopt a balanced Slice Wasserstein distance as the metric for unsupervised domain adaptation to solve this problem. Multiple standard datasets for domain adaptation and X-ray datasets of different Covid-19 are adopted to verify the effectiveness of our proposed method. Experimented by cross-adopting multiple datasets as source and target domains, respectively, our proposed method can effectively capture discriminative and domain-invariant representations with better data distribution matching.