Table Structure Recognition (TSR) aims to extract the bounding boxes of cells and table structure (e.g., HTML) from table images. Although current approaches have made significant progress, the latest image-to-sequence methods overlook the explicit utilization of the bounding box information when predicting HTML sequences, leading to error predictions in complex scenes. In this paper, we introduce a novel framework BGTR (Bounding Box-Guided Table Recognizer). To more effectively utilize bounding box information, we first predict the bounding boxes of cells and then use this information to guide the generation of HTML sequences. While utilizing bounding box information can enhance the accuracy of HTML sequences, for natural scene tables, the data volume is too small to allow for sufficient training of bbox-guided HTML generation. In response, we adopt a progressive training method for natural scene tables and introduce SNSTab, a synthetically generated natural scene table dataset. Our experiments on five benchmark datasets demonstrate SOTA performance.