Most existing matching algorithms are one-off algorithms, i.e., they usually measure the distance between the two image feature representation vectors for only one time. In contrast, human's vision system achieves this task, i.e., image matching, by recursively looking at specific/related parts of both images and then making the final judgement. Towards this end, we propose a novel loopy recurrent neural network (Loopy RNN), which is capable of aggregating relationship information of two input images in a progressive/iterative manner and outputting the consolidated matching score in the final iteration. A Loopy RNN features two uniqueness. First, built on conventional long short-term memory (LSTM) nodes, it links the output gate of the tail node to the input gate of the head node, thus it brings up symmetry property required for matching. Second, a monotonous loss designed for the proposed network guarantees increasing confidence during the recursive matching process. Extensive experiments on several image matching benchmarks demonstrate the great potential of the proposed method.