Domain adaptation aims to generalise a high-performance learner on target domain (non-labelled data) by leveraging the knowledge from source domain (rich labelled data) which comes from a different but related distribution. Assuming the source and target domains data(e.g. images) come from a joint distribution but follow on different marginal distributions, the domain adaptation work aims to infer the joint distribution from the source and target domain to learn the domain invariant features. Therefore, in this study, I extend the existing state-of-the-art approach to solve the domain adaptation problem. In particular, I propose a new approach to infer the joint distribution of images from different distributions, namely Wasserstein Distance Guided Cross-Domain Learning (WDGCDL). WDGCDL applies the Wasserstein distance to estimate the divergence between the source and target distribution which provides good gradient property and promising generalisation bound. Moreover, to tackle the training difficulty of the proposed framework, I propose two different training schemes for stable training. Qualitative results show that this new approach is superior to the existing state-of-the-art methods in the standard domain adaptation benchmark.