Recent advances in Large Multimodal Models (LMMs) have revolutionized their reasoning and Optical Character Recognition (OCR) capabilities. However, their complex logical reasoning performance on text-rich images remains underexplored. To bridge this gap, we introduce LogicOCR, a benchmark comprising 2780 questions with two subsets, i.e., LogicOCR-Gen with 1100 multi-choice questions on generated images, and LogicOCR-Real with 1680 meticulously designed free-form questions on real-world images. For constructing LogicOCR-Gen, we first curate a text corpus from the Chinese National Civil Servant Examination, and customize an automatic pipeline to steer GPT-Image-1 to generate images with varied layouts and fonts, ensuring contextual relevance and visual realism. Then, the generated images are manually verified. We evaluate a range of representative LMMs under Chain-of-Thought (CoT) and direct-answer settings. Our multi-dimensional analysis reveals key insights, such as the impact of test-time scaling, input modality differences, and sensitivity to visual-text orientation. Notably, LMMs still lag in multimodal reasoning compared to text-only inputs, indicating that they have not fully bridged visual reading with reasoning. Moreover, we propose TextCue, a training-free method that enhances LMMs' perception of image regions containing important text cues for solving questions. We leverage LMMs' attention maps and an off-the-shelf text segmentation specialist to determine the region, which is then cropped and enlarged to augment the original image. Experiments show its effectiveness, e.g., a 1.8% accuracy gain over LLaVA-OV-1.5-8B under the CoT setting. Our benchmark is available at https://github.com/MiliLab/LogicOCR.