Feature Matching has long been the basis and a central topic in the field of computer vision and image processing. SIFT (scale-invariant feature transformation, by David G. Lowe), due to its advantages of invariance to image scale and rotation, and robustness to a substantial range of affine distortion and change in viewpoint, has been attracting the attention of many domestic and foreign researchers over a decade. Rapidity and accuracy are very crucial for stereo pairwise image matching in applications such as 3D reconstruction. First, in order to accelerate the speed and promote the accuracy of matching, this paper proposes a novel method based on SIFT called approximately consistent in orientation (ACIO), which depicts the spatial location relationship of two matched vectors between stereo pairwise images (SPI), and therefore improves the accuracy of matching efficiently by avoiding the wrong correspondences. Secondly, this paper analyzes the structure of standard K-d tree (SKD-tree) and proposes a new one with hierarchical structure, named HKD-tree, which partitions the feature sets of SPI into stripes in terms of ACIO constraint and builds map between them. By reducing the search space, the matching speed increases greatly. Thirdly this work presents an efficient and fast matching algorithm based on ACIO and HKD-tree. Extensive trials based on a benchmark data set show that the proposed approach outperforms the state-of-the-art methods in matching speed with slight promotion in accuracy. Particulary, it is one order of magnitude faster than SKD-tree and also several times against the recent CasHash method.