The feature analysis of point clouds, a popular representation of three‐dimensional (3D) objects, is rising as a hot research topic nowadays. Point cloud data bear a sparse and unordered nature, making many commonly used feature extraction methods, for example, Convolutional Neural Networks (CNNs) inapplicable, while previous models suitable for the task are usually complex. We aim to reduce model complexity by reducing the number of parameters while achieving better (or at least comparable) performance. We propose an Interpolation Graph Convolutional Network (IGCN) for extracting features of point clouds. IGCN uses the point cloud graph structure and a specially designed Interpolation Convolution Kernel to mimic the operations of CNN for feature extraction. On the basis of weight postfusion and multilevel‐resolution aggregation, IGCN not only reduces the cost of calculating the interpolation operation but also improves the model's performance. We validate the performance of IGCN on both point cloud classification and segmentation tasks and explore the contribution of each module of our model through ablation experiments. Furthermore, we embed the IGCN point cloud feature extraction module as a plug‐and‐play module into other frameworks and perform point cloud registration experiments.