Features play an important role in the prediction tasks of e-commerce recommendations. To guarantee the consistency of off-line training and on-line serving, we usually utilize the same features that are both available. However, the consistency in turn neglects some discriminative features. For example, when estimating the conversion rate (CVR), i.e., the probability that a user would purchase the item if she clicked it, features like dwell time on the item detailed page are informative. However, CVR prediction should be conducted for on-line ranking before the click happens. Thus we cannot get such post-event features during serving. We define the features that are discriminative but only available during training as the privileged features. Inspired by the distillation techniques which bridge the gap between training and inference, in this work, we propose privileged features distillation (PFD). We train two models, i.e., a student model that is the same as the original one and a teacher model that additionally utilizes the privileged features. Knowledge distilled from the more accurate teacher is transferred to the student to improve its accuracy. During serving, only the student part is extracted and it relies on no privileged features. We conduct experiments on two fundamental prediction tasks at Taobao recommendations, i.e., click-through rate (CTR) at coarse-grained ranking and CVR at fine-grained ranking. By distilling the interacted features that are prohibited during serving for CTR and the post-event features for CVR, we achieve significant improvements over their strong baselines. During the on-line A/B tests, the click metric is improved by +5.0% in the CTR task. And the conversion metric is improved by +2.3% in the CVR task. Besides, by addressing several issues of training PFD, we obtain comparable training speed as the baselines without any distillation.