Semi-supervised learning and active learning are important techniques to build more accurate model while labeled data are scarce. The objective of this paper is combining both to effectively relieve user labor for multi-class annotation. We propose a novel graph-based active semi-supervised learning framework which aim at efficiently learning a multi-class model with minimal human labor. In particular, we propose Minimize Expected Global Uncertainty algorithm to actively select examples (for labels), which naturally integrates with the probabilistic results of graph-based semi-supervised learning. Meanwhile, we update the model incrementally by decomposed formulation while the new example are incorporated for training, which only has the time complexity of O(n), compared to the original re-training of O(n³). Extensive evaluations over three real-world datasets demonstrate that our proposed method has the superior performance comparing with the baselines and the capability to efficiently build more accurate model with fractional human labor.