In practice, the circumstance that training and test data are clean is not always satisfied. The performance of existing methods in the learning using privileged information (LUPI) paradigm may be seriously challenged, due to the lack of clear strategies to address potential noises in the data. This paper proposes a novel Robust SVM+ (RSVM+) algorithm based on a rigorous theoretical analysis. Under the SVM+ framework in the LUPI paradigm, we study the lower bound of perturbations of both example feature data and privileged feature data, which will mislead the model to make wrong decisions. By maximizing the lower bound, tolerance of the learned model over perturbations will be increased. Accordingly, a novel regularization function is introduced to upgrade a variant form of SVM+. The objective function of RSVM+ is transformed into a quadratic programming problem, which can be efficiently optimized using off-the-shelf solvers. Experiments on real-world datasets demonstrate the necessity of studying robust SVM+ and the effectiveness of the proposed algorithm.