The spiking neural networks (SNNs), as brain- inspired neural networks, have received noteworthy attention due to their advantages of low power consumption, high parallelism, and high fault tolerance. While SNNs have shown promising results in uni-modal data tasks, their deployment in multi-modal audiovisual classification remains limited, and the effectiveness of capturing correlations between visual and audio modalities in SNNs needs improvement. To address these challenges, we propose a novel model called Spiking Multi-Model Transformer (SMMT) that combines SNNs and Transformers for multi-modal audiovisual classification. The SMMT model integrates uni- modal sub-networks for visual and auditory modalities with a novel Spiking Cross-Attention module for fusion, enhancing the correlation between visual and audio modalities. This approach leads to competitive accuracy in multi-modal classification tasks with low energy consumption, making it an effective and energy- efficient solution. Extensive experiments on a public event-based dataset(N-TIDIGIT&MNIST-DVS) and two self-made audiovisual datasets of real-world objects(CIFAR10-AV and UrbanSound8K- AV) demonstrate the effectiveness and energy efficiency of the proposed SMMT model in multi-modal audio-visual classification tasks. Our constructed multi-modal audiovisual datasets can be accessed at https://github.com/Guo-Lingyue/SMMT.