Stylized dialogue generation, which aims to generate a given-style response for an input context, plays a vital role in intelligent dialogue systems. Considering there is no parallel data between the contexts and the responses of target style S1, existing works mainly use back translation to generate stylized synthetic data for training, where the data about context, target style S1 and an intermediate style S0 is used. However, the interaction among these texts is not fully exploited, and the pseudo contexts are not adequately modeled. To overcome the above difficulties, we propose multi-pass dual learning (MPDL), which leverages the duality among the context, response of style S1 and response of style S_0. MPDL builds mappings among the above three domains, where the context should be reconstructed by the MPDL framework, and the reconstruction error is used as the training signal. To evaluate the quality of synthetic data, we also introduce discriminators that effectively measure how a pseudo sequence matches the specific domain, and the evaluation result is used as the weight for that data. Evaluation results indicate that our method obtains significant improvement over previous baselines.