Recent advancements in optical flow estimation have led to notable performance gains,driven by the adoption of transformer architectures, enhanced data augmentation, self-supervised learningtechniques, the use of multiple video frames and iterative refinement of estimate optical flows. Nonetheless,these cutting-edge methods encounter substantial challenges with surge in computational complexity andmemory demands. In response, we introduce a lightweight optical flow method, called MaxFlow, to addressthe trade-off between computational complexity and prediction performance. By leveraging MaxViT,we design a network with a global receptive field at reduced complexity, and proposed 1D matching toalleviate the computational complexity from (HxW)2toHxW(H+W), wherHandWdenotesheight and width of input image. Consequently, our method achieves the lowest computational complexitycompared to both state of the arts(SOTA) and other lightweight optical flow estimation methods, whilestill achieving competitive results with the SOTA techniques. We performed extensive experiments to showthe effectiveness of our method, achieving about 5 to 6 times reductions in computation complexity whilemaintaining the prediction accuracy with only degradation of 16% in term of end point error(EPE) at Sinteltest clean sequences with respect to RAFT method.