The soaring demand for intelligent mobile applications calls for deploying powerful deep neural networks (DNNs) on mobile devices. However, the outstanding performance of DNNs notoriously relies on increasingly complex models, which in turn is associated with an increase in computational expense far surpassing mobile devices’ capacity. What is worse, app service providers need to collect and utilize a large volume of users’ data, which contain sensitive information, to build the sophisticated DNN models. Directly deploying these models on public mobile devices presents prohibitive privacy risk. To benefit from the on-device deep learning without the capacity and privacy concerns, we design a private model compression framework RONA. Following the knowledge distillation paradigm, we jointly use hint learning, distillation learning, and self learning to train a compact and fast neural network. The knowledge distilled from the cumbersome model is adaptively bounded and carefully perturbed to enforce differential privacy. We further propose an elegant query sample selection method to reduce the number of queries and control the privacy loss. A series of empirical evaluations as well as the implementation on an Android mobile device show that RONA can not only compress cumbersome models efficiently but also provide a strong privacy guarantee. For example, on SVHN, when a meaningful (9.83,10−6)-differential privacy is guaranteed, the compact model trained by RONA can obtain 20× compression ratio and 19× speed-up with merely 0.97% accuracy loss.