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The constraint of neighborhood consistency or local consistency is widely used for robust image matching. In this paper, we focus on learning neighborhood topology consistent descriptors (TCDesc), while former works of learning descriptors, such as HardNet and DSM, only consider point-to-point Euclidean distance among descriptors and totally neglect neighborhood information of descriptors. To learn topology consistent descriptors, first we propose the linear combination weights to depict the topological relationship between center descriptor and its kNN descriptors, where the difference between center descriptor and the linear combination of its kNN descriptors is minimized. Then we propose the global mapping function which maps the local linear combination weights to the global topology vector and define the topology distance of matching descriptors as l1 distance between their topology vectors. Last we employ adaptive weighting strategy to jointly minimize topology distance and Euclidean distance, which automatically adjust the weight or attention of two distances in triplet loss. Our method has the following two advantages: (1) We are the first to consider neighborhood information of descriptors, while former works mainly focus on neighborhood consistency of feature points; (2) Our method can be applied in any former work of learning descriptors by triplet loss. Experimental results verify the generalization of our method: We can improve the performances of both HardNet and DSM on several benchmarks.