This paper targets at a new and challenging setting of knowledge transfer from multiple source domains to a single target domain, where target data is few shot or even one shot with label. Traditional domain generalization or adaptation methods cannot directly work since there is no sufficient target domain distribution serving as the transfer object. The multi-source setting further prevents the transfer task as excessive domain gap introduced from all the source domains. To tackle this problem, we newly propose a progressive mix-up (P-Mixup) mechanism to introduce an intermediate mix-up domain, pushing both the source domains and the few-shot target domain aligned to this mix-up domain. Further by enforcing the mix-up domain to progressively move towards the source domains, we achieve the domain transfer from multi-source domains to the single one-shot target domain. Our P-Mixup is different from traditional mix-up that ours is with a progressive and adaptive mix-up ratio, following the curriculum learning spirit to better align the source and target domains. Moreover, our P-Mixup combines both pixel-level and feature-level mix-up to better enrich the data diversity. Experiments on two benchmarks show that our P-Mixup significantly outperforms the state-of-the-art methods, i.e., 6.0\% and 6.8\% improvements on Office-Home and DomainNet.