Long non-coding RNA (IncRNA) has a close relationship with multiple biological processes and complex diseases. Generally speaking, it functions through the interaction with corresponding RNA-binding proteins. However, it is costly and time-consuming to use experimental methods to detect IncRNA-protein interactions. Network-based prediction methods have been developed recently, but very few methods consider the integration of multiple features and the non-linear relationship of IncRNAs (proteins). In this paper, we propose a kernel-based soft-neighborhood propagation algorithm (LKSNS) to predict the potential IncRNA-protein interactions. The method not only makes use of the non-neighborhood information, but also excavates the potential non-linear relationship. We compare LKSNS with other state-of-the-art methods based on multiple datasets and the results show that LKSNS has significantly better prediction performance. The case study further demonstrates that the LKSNS has the good practicality for IncRNA-protein interaction prediction.