We consider two biologically plausible structures, the Spiking Neural Network (SNN) and the self-attention mechanism. The former offers an energy-efficient and event-driven paradigm for deep learning, while the latter has the ability to capture feature dependencies, enabling Transformer to achieve good performance. It is intuitively promising to explore the marriage between them. In this paper, we consider leveraging both self-attention capability and biological properties of SNNs, and propose a novel Spiking Self Attention (SSA) as well as a powerful framework, named Spiking Transformer (Spikformer). The SSA mechanism in Spikformer models the sparse visual feature by using spike-form Query, Key, and Value without softmax. Since its computation is sparse and avoids multiplication, SSA is efficient and has low computational energy consumption. It is shown that Spikformer with SSA can outperform the state-of-the-art SNNs-like frameworks in image classification on both neuromorphic and static datasets. Spikformer (66.3M parameters) with comparable size to SEW-ResNet-152 (60.2M,69.26%) can achieve 74.81% top1 accuracy on ImageNet using 4 time steps, which is the state-of-the-art in directly trained SNNs models. Code is avaiable at https://github.com/ZK-Zhou/spikformer.