This paper introduces Point-GN, a novel non-parametric network for efficient and accurate 3D point cloud classification. Unlike conventional deep learning models that rely on a large number of trainable parameters, Point-GN leverages non-learnable components-specifically, Farthest Point Sampling (FPS), k-Nearest Neighbors (k-NN), and Gaussian Positional Encoding (GPE)-to extract both local and global geometric features. This design eliminates the need for additional training while maintaining high performance, making Point-GN particularly suited for real-time, resource-constrained applications. We evaluate Point-GN on two benchmark datasets, ModelNet40 and ScanObjectNN, achieving classification accuracies of 85.29% and 85.89%, respectively, while significantly reducing computational complexity. Point-GN outperforms existing non-parametric methods and matches the performance of fully trained models, all with zero learnable parameters. Our results demonstrate that Point-GN is a promising solution for 3D point cloud classification in practical, real-time environments.