By transferring knowledge from the abundant labeled samples of known source classes, zero-shot learning (ZSL) makes it possible to train recognition models for novel target classes that have no labeled samples. Conventional ZSL approaches usually adopt a two-step recognition strategy, in which the test sample is projected into an intermediary space in the first step, and then the recognition is carried out by considering the similarity between the sample and target classes in the intermediary space. Due to this redundant intermediate transformation, information loss is unavoidable, thus degrading the performance of overall system. Rather than adopting this two-step strategy, in this paper, we propose a novel one-step recognition framework that is able to perform recognition in the original feature space by using directly trained classifiers. To address the lack of labeled samples for training supervised classifiers for the target classes, we propose to transfer samples from source classes with pseudo labels assigned, in which the transferred samples are selected based on their transferability and diversity. Moreover, to account for the unreliability of pseudo labels of transferred samples, we modify the standard support vector machine formulation such that the unreliable positive samples can be recognized and suppressed in the training phase. The entire framework is fairly general with the possibility of further extensions to several common ZSL settings. Extensive experiments on four benchmark data sets demonstrate the superiority of the proposed framework, compared with the state-of-the-art approaches, in various settings.