The interactions between non-coding RNAs (ncRNAs) and proteins play an important role in many biological processes, and their biological functions are primarily achieved by binding with a variety of proteins. High-throughput biological techniques are used to identify protein molecules bound with specific ncRNA, but they are usually expensive and time consuming. Deep learning provides a powerful solution to computationally predict RNA-protein interactions. In this work, we propose the RPI-SAN model by using the deep-learning stacked auto-encoder network to mine the hidden high-level features from RNA and protein sequences and feed them into a random forest (RF) model to predict ncRNA binding proteins. Stacked assembling is further used to improve the accuracy of the proposed method. Four benchmark datasets, including RPI2241, RPI488, RPI1807, and NPInter v2.0, were employed for the unbiased evaluation of five established prediction tools: RPI-Pred, IPMiner, RPISeq-RF, IncPro, and RPI-SAN. The experimental results show that our RPI-SAN model achieves much better performance than other methods, with accuracies of 90.77%, 89.7%, 96.1%, and 99.33%, respectively. It is anticipated that RPI-SAN can be used as an effective computational tool for future biomedical researches and can accurately predict the potential ncRNA-protein interacted pairs, which provides reliable guidance for biological research.