Extracting informative local features in point clouds is crucial for accurately understanding spatial information inside 3D point data. Previous works utilize either complex network designs or simple multi-layer perceptrons (MLP) to extract the local features. However, complex networks often incur high computational cost, whereas simple MLP may struggle to capture the spatial relations among local points effectively. These challenges limit their scalability to delicate and real-time tasks, such as autonomous driving and robot navigation. To address these challenges, we propose a novel 3D Directional Encoding Network (3D-DENet) capable of effectively encoding spatial relations with low computational cost. 3D-DENet extracts spatial and point features separately. The key component of 3D-DENet for spatial feature extraction is Directional Encoding (DE), which encodes the cosine similarity between direction vectors of local points and trainable direction vectors. To extract point features, we also propose Local Point Feature Multi-Aggregation (LPFMA), which integrates various aspects of local point features using diverse aggregation functions. By leveraging DE and LPFMA in a hierarchical structure, 3D-DENet efficiently captures both detailed spatial and high-level semantic features from point clouds. Experiments show that 3D-DENet is effective and efficient in classification and segmentation tasks. In particular, 3D-DENet achieves an overall accuracy of 90.7% and a mean accuracy of 90.1% on ScanObjectNN, outperforming the current state-of-the-art method while using only 47% floating point operations.