Recently, convolutional neural networks (CNNs) have achieved an appealing performance in hyperspectral image (HSI) classification. Although CNNs excel at capturing local details, they fall short in modeling long-range dependencies due to small receptive fields. Spiking neural networks (SNNs) simulate the encoding and processing of information by the human brain, increasing the receptive field when extracting image features, which is expected to solve the previous problems. Therefore, we present further study on exploiting the power of SNNs for axial global information interaction. The proposed approach, termed Hyper-S3NN, combines CNNs and SNNs to leverage the fine localization information and global contexts. Specifically, based on the leaky integrate-and-fire (LIF) neurons in SNNs, three types of LIF branches are proposed to obtain the global interactive features along the horizontal, vertical, and channel dimensions. By combining convolutions for local information extraction and feature fusion, our Spatial–Spectral LIF (SSLIF) module can effectively integrate these three-dimensional features and enhance the local detail representation capability of the model. Extensive experiments conducted on four benchmark datasets for HSI task (Pavia University, Indian Pines, Trento and Houston 2013) indicate that our method achieves state-of-the-art (SOTA) performance compared with previous methods, which demonstrates the superiority and robust generalization capability of our Hyper-S3NN.