With the increasing data dimensionality, feature selection has become a fundamental task to deal with high-dimensional data. Semi-supervised feature selection focuses on the problem of how to learn a relevant feature subset in the case of abundant unlabeled data with few labeled data. In recent years, many semi-supervised feature selection algorithms have been proposed. However, these algorithms are implemented by separating the processes of feature selection and classifier training, such that they cannot simultaneously select features and learn a classifier with the selected features. Moreover, they ignore the difference of reliability inside unlabeled samples and directly use them in the training stage, which might cause performance degradation. In this paper, we propose a joint semi-supervised feature selection and classification algorithm (JSFS) which adopts a Bayesian approach to automatically select the relevant features and simultaneously learn a classifier. Instead of using all unlabeled samples indiscriminately, JSFS associates each unlabeled sample with a self-adjusting weight to distinguish the difference between them, which can effectively eliminate the irrelevant unlabeled samples via introducing a left-truncated Gaussian prior. Experiments on various datasets demonstrate the effectiveness and superiority of JSFS.