This paper presents Neighbor-Guided SemiGlobal Matching (NG-fSGM), a new method for optical flow. It is based on SGM, a popular dynamic programming algorithm for stereo vision, where the disparity of each pixel is calculated by aggregating local matching costs over the entire image to resolve local ambiguity in texture-less and occluded regions. Unlike conventional SGM, NG-fSGM operates on a subset of the search space that has been aggressively pruned based on neighboring pixels' information. Our proposed method achieves a fast approximation of SGM with significantly simpler cost aggregation and flow computation. Compared to a prior SGM extension for optical flow, the proposed NG-fSGM provides about 9x reduction in the number of computations and 5x reduction in the memory requirement with only 0.17% accuracy degradation when evaluated with Middlebury benchmark test cases.