Unsupervised dependency parsing aims to learn a dependency parser from unannotated sentences. Existing work focuses on either learning generative models using the expectation-maximization algorithm and its variants, or learning discriminative models using the discriminative clustering algorithm. In this paper, we propose a new learning strategy that learns a generative model and a discriminative model jointly based on the dual decomposition method. Our method is simple and general, yet effective to capture the advantages of both models and improve their learning results. We tested our method on the UD treebank and achieved a state-of-the-art performance on thirty languages.