Spiking transformers have recently emerged as a robust alternative in deep learning. One focus of this field is the reduction of energy consumption, given that spiking transformers require lengthy simulation timesteps and complex floating-point attention mechanisms. In this paper, we propose a one-step approach that requires only one timestep and is of linear complexity. The proposed One-step Spiking Transformer (OST) incorporates a Time Domain Compression and Compensation (TDCC) component, which can significantly mitigate the spatio-temporal overhead of spiking transformers. Another novel component in OST is the Spiking Linear Transformation (SLT), designed to greatly reduce the number of floating-point multiply-and-accumulate operations. Experiments on both static and neuromorphic images show that OST can perform as well as or better than SOTA methods with just one timestep, even for more difficult tasks. For instance, comparing with Spikeformer, OST gains 1.59% in accuracy on ImageNet, yet 40.27% more efficient, and gains 0.7% on DVS128 Gesture. The supplementary materials and source code are available at https://github.com/songxt3/OST.