Multi-graph multi-label learning (\textsc{Mgml}) is a supervised learning framework, which aims to learn a multi-label classifier from a set of labeled bags each containing a number of graphs. Prior techniques on the \textsc{Mgml} are developed based on transfering graphs into instances and focus on learning the unseen labels only at the bag level. In this paper, we propose a \textit{coarse} and \textit{fine-grained} Multi-graph Multi-label (cfMGML) learning framework which directly builds the learning model over the graphs and empowers the label prediction at both the \textit{coarse} (aka. bag) level and \textit{fine-grained} (aka. graph in each bag) level. In particular, given a set of labeled multi-graph bags, we design the scoring functions at both graph and bag levels to model the relevance between the label and data using specific graph kernels. Meanwhile, we propose a thresholding rank-loss objective function to rank the labels for the graphs and bags and minimize the hamming-loss simultaneously at one-step, which aims to addresses the error accumulation issue in traditional rank-loss algorithms. To tackle the non-convex optimization problem, we further develop an effective sub-gradient descent algorithm to handle high-dimensional space computation required in cfMGML. Experiments over various real-world datasets demonstrate cfMGML achieves superior performance than the state-of-arts algorithms.