High-speed railways have been one of the most popular means of transportation all over the world. As an important part of the high-speed railway power supply system, the overhead catenary system (OCS) directly influences the stable operation of the railway, so regular inspection and maintenance are essential. Now manual inspection is too inefficient and high-cost to fit the requirements for high-speed railway operation, and automatic inspection becomes a trend. The 3D information in the point cloud is useful for geometric parameter measurement in the catenary inspection. Thus it is significant to recognize the components of OCS from the point cloud data collected by the inspection equipment, which promotes the automation of parameter measurement. In this paper, we present a novel method based on deep learning to recognize point clouds of OCS components. The method identifies the context of each single frame point cloud by a convolutional neural network (CNN) and combines some single frame data based on classification results, then inputs them into a segmentation network to identify OCS components. To verify the method, we build a point cloud dataset of OCS components that contains eight categories. The experimental results demonstrate that the proposed method can detect OCS components with high accuracy. Our work can be applied to the real OCS components detection and has great practical significance for OCS automatic inspection.