The Vision Transformer (ViT) has achieved remarkable success in computer vision due to its powerful token mixer, which effectively captures global dependencies among all tokens. However, the quadratic complexity of standard self-attention with respect to the number of tokens severely hampers its computational efficiency in practical deployment. Although recent hybrid approaches have sought to combine the strengths of convolutions and self-attention to improve the performance-efficiency trade-off, the costly pairwise token interactions and heavy matrix operations in conventional self-attention remain a critical bottleneck. To overcome this limitation, we introduce S2AFormer, an efficient Vision Transformer architecture built around a novel Strip Self-Attention (SSA) mechanism. Our design incorporates lightweight yet effective Hybrid Perception Blocks (HPBs) that seamlessly fuse the local inductive biases of CNNs with the global modeling capability of Transformer-style attention. The core innovation of SSA lies in simultaneously reducing the spatial resolution of the key ( $K$ ) and value ( $V$ ) tensors while compressing the channel dimension of the query ( $Q$ ) and key ( $K$ ) tensors. This joint spatial-and-channel compression dramatically lowers computational cost without sacrificing representational power, achieving an excellent balance between accuracy and efficiency. We extensively evaluate S2AFormer on a wide range of vision tasks, including image classification (ImageNet-1K), semantic segmentation (ADE20K), and object detection/instance segmentation (COCO). Experimental results consistently show that S2AFormer delivers substantial accuracy improvements together with superior inference speed and throughput across both GPU and non-GPU platforms, establishing it as a highly competitive solution in the landscape of efficient Vision Transformers.