Reaching a human-level understanding of real-world documents necessitates effective machine reading comprehension, yet recent developments in this area often struggle with table images. In response, we introduce the Visual Table Reading Comprehension (TabComp) dataset, which includes table images, questions, and generative answers designed to evaluate OCR-free models. Unlike general Visual Question Answering (VQA) datasets, TabComp uniquely focuses on table images, fostering the development of systems which obviate the use of optical character recognition (OCR) technology, which often struggles with complex table layouts. Our findings reveal that current OCR-free models perform poorly on TabComp, highlighting the need for robust, specialized models for accurate table reading comprehension. We propose TabComp as a benchmark for evaluating OCR-free models in table reading comprehension and encourage the research community to collaborate on developing more effective solutions. The code and data are available at - https://github.com/dialabiitj/TabComp/