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Open-set recognition (OSR) aims to simultaneously detect unknown-class samples and classify known-class samples. Most of the existing OSR methods are inductive methods, which generally suffer from the domain shift problem that the learned model from the known-class domain might be unsuitable for the unknown-class domain. Addressing this problem, inspired by the success of transductive learning for alleviating the domain shift problem in many other visual tasks, we propose an Iterative Transductive OSR framework, called IT-OSR, which implements three explored modules iteratively, including a reliability sampling module, a feature generation module, and a baseline update module. Specifically, at each iteration, a dual-space consistent sampling approach is presented in the explored reliability sampling module for selecting some relatively more reliable ones from the test samples according to their pseudo labels assigned by a baseline method, which could be an arbitrary inductive OSR method. Then, a conditional dual-adversarial generative network under an orthogonal coding condition is designed in the feature generation module to generate discriminative sample features of both known and unknown classes according to the selected test samples with their pseudo labels. Finally, the baseline method is updated for sample re-prediction in the baseline update module by jointly utilizing the generated features, the selected test samples with pseudo labels, and the training samples. Extensive experimental results on both the standard-dataset and the cross-dataset settings demonstrate that the derived transductive methods, by introducing two typical inductive OSR methods into the proposed IT-OSR framework, achieve better performances than 15 state-of-the-art methods in most cases.