Distributed representations of words which map each word to a continuous vector have proven useful in capturing important linguistic information not only in a single language but also across different languages. Current unsupervised adversarial approaches show that it is possible to build a mapping matrix that aligns two sets of monolingual word embeddings without high quality parallel data, such as a dictionary or a sentence-aligned corpus. However, without an additional step of refinement, the preliminary mapping learnt by these methods is unsatisfactory, leading to poor performance for typologically distant languages. In this paper, we propose a weakly-supervised adversarial training method to overcome this limitation, based on the intuition that mapping across languages is better done at the concept level than at the word level. We propose a concept-based adversarial training method which improves the performance of previous unsupervised adversarial methods for most languages, and especially for typologically distant language pairs.