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Unsupervised domain adaptation (UDA) has attracted considerable attention, which transfers knowledge from a label-rich source domain to a related but unlabeled target domain. Reducing inter-domain differences has always been a crucial factor to improve performance in UDA, especially for tasks where there is a large gap between source and target domains. To this end, we propose a novel style-aware feature fusion method (SAFF) to bridge the large domain gap and transfer knowledge while alleviating the loss of class-discriminative information. Inspired by the human transitive inference and learning ability, a novel style-aware self-intermediate domain (SSID) is investigated to link two seemingly unrelated concepts through a series of intermediate auxiliary synthesized concepts. Specifically, we propose a novel learning strategy of SSID, which selects samples from both source and target domains as anchors, and then randomly fuses the object and style features of these anchors to generate labeled and style-rich intermediate auxiliary features for knowledge transfer. Moreover, we design an external memory bank to store and update specified labeled features to obtain stable class features and class-wise style features. Based on the proposed memory bank, the intra- and inter-domain loss functions are designed to improve the class recognition ability and feature compatibility, respectively. Meanwhile, we simulate the rich latent feature space of SSID by infinite sampling and the convergence of the loss function by mathematical theory. Finally, we conduct comprehensive experiments on commonly used domain adaptive benchmarks to evaluate the proposed SAFF, and the experimental results show that the proposed SAFF can be easily combined with different backbone networks and obtain better performance as a plug-in-plug-out module.