Tagging has become one of the most significant methods for information organization.With the proliferation of recommending systems, tag recommendation problem has attracted more and more attention from researchers.Currently, while a variety of tagging systems exist, as the system function becomes more and more complex, the information of tagging data generated by tagging system becomes increasingly complex.In this paper, a tagging system is modeled as a heterogeneous network.To learn the importance of different types of nodes and edges, a general graph-based model, called HnMTR, is proposed.First, HnMTR maps different heterogeneous objects into a unified space so that objects from different dimensions can be directly compared.Then multivariate Markov model is applied to the mapped network to rank tag nodes.Highly ranked tags are recommended for the user.Experiments on three real world datasets with different tagging behavior demonstrate that the proposed method outperforms the state-of-the-art methods significantly.