Long non-coding RNAs (LncRNAs) play important roles in a series of life activities, and they function primarily with proteins. The wet experimental-based methods in lncRNA-protein interactions (lncRPIs) study are time-consuming. Therefore, in this study, we propose a reliable computational-based method called LPI-CSFFR using sequences, secondary structures, and physicochemical properties of proteins and lncRNAs for training and predicting LncRPIs. Combining Serial Fusion with Feature Reuse is utilized based on the deep learning convolution neural network (CNN) algorithm. The experimental results indicate that LPI-CSFFR achieves superior performance on benchmark datasets RPI1460 and RPI1807 with an accuracy of 83.1% and 98%, respectively. We further compare LPI-CSFFR with the state-of-the-art existing methods on the same benchmark datasets to evaluate the performance. In addition, we predict the independent RPI9373 dataset using the model trained on RPI1460. The results show that LPI-CSFFR is promising for predicting LncRPIs. The source code of LPI-CSFFR and the datasets used in this study are available at https://github.com/JianjunTan-Beijing/LPI-CSFFR.