Audio-visual zero-shot learning (ZSL), which learns to classify video data from the classes not being observed during training, is challenging. In audio-visual ZSL, both semantic and temporal information from different modalities is relevant to each other. However, effectively extracting and fusing information from audio and visual remains an open challenge. In this work, we propose an Audio-Visual Modality-fusion Spiking Transformer network (AVMST) for audio-visual ZSL. To be more specific, AVMST provides a spiking neural network (SNN) module for extracting conspicuous temporal information of each modality, a cross-attention block to effectively fuse the temporal and semantic information, and a transformer reasoning module to further explore the interrelationships of fusion features. To provide robust temporal features, the spiking threshold of the SNN module is adjusted dynamically based on the semantic cues of different modalities. The generated feature map is in accordance with the zero-shot learning property thanks to our proposed spiking transformer's ability to combine the robustness of SNN feature extraction and the precision of transformer feature inference. Extensive experiments on three benchmark audiovisual datasets (i.e., VGGSound, UCF and ActivityNet) validate that the proposed AVMST outperforms existing state-of-the-art methods by a significant margin. The code and pre-trained models are available at https://github.com/liwr-hit/ICME23_AVMST.