Multi-source domain adaptation addresses the problem of transferring knowledge from multiple source domains to a target domain. Compared with conventional domain adaptation with single source and target domain, multi-source domain adaptation is more challenging because there are discrepancies not only across the source domains and the target domain, but also in source domains themselves. Hence, previous single-source domain adaptation methods may be suboptimal in handling multi-source scenarios. In this paper, we propose a multi-source domain adaptation method with graph embedding and adaptive label prediction to tackle the challenge. Specifically, our method leverages subspace learning and label prediction to mitigate both the inter-domain and intra-domain discrepancies. From the view of probability distribution, we match the first-order moment maximum mean discrepancy (MMD) to reduce the distribution divergence. From the view of sample relationship, we deploy graph embedding to preserve the similarity and discriminability of samples from different domains. Moment matching and geometry alignment are optimized in a unified objective to learn a subspace where both inter-domain and intra-domain discrepancies are reduced. For the label prediction, with the new representations learned in the subspace, we utilize K-means clustering and structural risk minimization (SRM) to predict pseudo labels in both low-dimensional subspace and high-dimensional RKHS. Specifically, we report two different strategies (denoted as ALP-u and ALP-s, respectively) for pseudo-labeling in this paper. The proposed ALP-u and ALP-s are effective in different kinds of domain adaptation scenarios, including multi-source and single-source domain adaptation. Experiments on three benchmark datasets verify that our ALP-u and ALP-s can outperform state-of-the-arts by a large margin.