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 the initialization stage, a baseline method, which could be an arbitrary inductive OSR method, is used for assigning pseudo labels to the test samples. At the iteration stage, based on the consistency of the assigned pseudo labels between the output/logit space and the latent feature space of the baseline method, a dual-space consistent sampling approach is presented in the reliability sampling module for sampling some reliable ones from the test samples. Then in the feature generation module, a conditional dual-adversarial generative network is designed to generate discriminative features of both known and unknown classes. This generative network employs two discriminators for implementing fake/real and known/unknown-class discriminations respectively. And it is trained by jointly utilizing the test samples with their pseudo labels selected in the reliability sampling module and the labeled training samples. Finally in the baseline update module, the above baseline method is updated/re-trained for sample re-prediction 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 19 state-of-the-art methods in most cases.