In this paper, we propose a weakly supervised multilingual representation learning framework, called cross-lingual self-training (XLST). XLST is able to utilize a small amount of annotated data from high-resource languages to improve the representation learning on multilingual un-annotated data. Specifically, XLST uses a supervised trained model to produce initial representations and another model to learn from them, by maximizing the similarity between output embeddings of these two models. Furthermore, the moving average mechanism and multi-view data augmentation are employed, which are experimentally shown to be crucial to XLST. Comprehensive experiments have been conducted on the CommonVoice corpus to evaluate the effectiveness of XLST. Results on 5 downstream low-resource ASR tasks shows that our multilingual pretrained model achieves relatively 18.6% PER reduction over the state-of-the-art self-supervised method, with leveraging additional 100 hours of annotated English data.