Spiking Neural Networks (SNNs) present a compelling and energy-efficient alternative to traditional Artificial Neural Networks (ANNs) due to their sparse binary activation. Leveraging the success of the transformer architecture, the spiking transformer architecture is explored to scale up dataset size and performance. However, existing works only consider the spatial self-attention in spiking transformer, neglecting the inherent temporal context across the timesteps. In this work, we introduce Spiking Transformer with Spatial-Temporal Attention (STAtten), a simple and straightforward architecture designed to integrate spatial and temporal information in self-attention with negligible additional computational load. The STAtten divides the temporal or token index and calculates the self-attention in a cross-manner to effectively incorporate spatial-temporal information. We first verify our spatial-temporal attention mechanism's ability to capture long-term temporal dependencies using sequential datasets. Moreover, we validate our approach through extensive experiments on varied datasets, including CIFAR10/100, ImageNet, CIFAR10-DVS, and N-Caltech101. Notably, our cross-attention mechanism achieves an accuracy of 78.39 % on the ImageNet dataset.