Given a query patch from a novel class, one-shot object detection aims to detect all instances of this class in a target image through the semantic similarity comparison. However, due to the extremely limited guidance in the novel class as well as the unseen appearance difference between the query and target instances, it is difficult to appropriately exploit their semantic similarity and generalize well. To mitigate this problem, we present a universal Cross-Attention Transformer (CAT) module for accurate and efficient semantic similarity comparison in one-shot object detection. The proposed CAT utilizes the transformer mechanism to comprehensively capture bi-directional correspondence between any paired pixels from the query and the target image, which empowers us to sufficiently exploit their semantic characteristics for accurate similarity comparison. In addition, the proposed CAT enables feature dimensionality compression for inference speedup without performance loss. Extensive experiments on three object detection datasets MS-COCO, PASCAL VOC and FSOD under the one-shot setting demonstrate the effectiveness and efficiency of our model, e.g., it surpasses CoAE, a major baseline in this task, by 1.0% in average precision (AP) on MS-COCO and runs nearly 2.5 times faster.