Automatic text summarization aims at producing a shorter version of the input text that conveys the most important information. However, multi-lingual text summarization, where the goal is to process texts in multiple languages and output summaries in the corresponding languages with a single model, has been rarely studied. In this paper, we present MultiSumm, a novel multi-lingual model for abstractive summarization. The MultiSumm model uses the following training regime: (I) multi-lingual learning that contains language model training, auto-encoder training, translation and back-translation training, and (II) joint summary generation training. We conduct experiments on summarization datasets for five rich-resource languages: English, Chinese, French, Spanish, and German, as well as two low-resource languages: Bosnian and Croatian. Experimental results show that our proposed model significantly outperforms a multi-lingual baseline model. Specifically, our model achieves comparable or even better performance than models trained separately on each language. As an additional contribution, we construct the first summarization dataset for Bosnian and Croatian, containing 177,406 and 204,748 samples, respectively.