Recently, the Vision Transformer (ViT) model has replaced the classical Convolutional Neural Network (ConvNet) in various computer vision tasks due to its superior performance. Even in hyperspectral image (HSI) classification field, ViT-based methods also show promising potential. Nevertheless, ViT encounters notable difficulties in processing HSI data. Its self-attention mechanism, which exhibits quadratic complexity, escalates computational costs. Additionally, ViT's substantial demand for training samples does not align with the practical constraints posed by the expensive labeling of HSI data. To overcome these challenges, we propose a 3D relational ConvNet named 3D-RCNet, which inherits both strengths of ConvNet and ViT, resulting in high performance in HSI classification. We embed the self-attention mechanism of Transformer into the convolutional operation of ConvNet to design 3D relational convolutional operation and use it to build the final 3D-RCNet. The proposed 3D-RCNet maintains the high computational efficiency of ConvNet while enjoying the flexibility of ViT. Additionally, the proposed 3D relational convolutional operation is a plug-and-play operation, which can be inserted into previous ConvNet-based HSI classification methods seamlessly. Empirical evaluations on three representative benchmark HSI datasets show that the proposed model outperforms previous ConvNet-based and ViT-based HSI approaches.