Fine-Grained Sketch-Based Image Retrieval (FG-SBIR) is to use free-hand sketches as queries to perform instance-level retrieval in an image gallery. Existing works usually leverage only high-level information and perform matching in a single region. However, both low-level and high-level information are helpful to establish fine-grained correspondence. Besides, we argue that matching different regions between each sketch-image pair can further boost model robustness. Therefore, we propose Multi-Level Region Matching (MLRM) for FG-SBIR, which consists of two modules: a Discriminative Region Extraction module (DRE) and a Region and Level Attention module (RLA). In DRE, we propose Light-weighted Attention Map Augmentation (LAMA) to extract local feature from different regions. In RLA, we propose a transformer-based attentive matching module to learn attention weights to explore different importance from different image/sketch regions and feature levels. Furthermore, to ensure that the geometrical and semantic distinctiveness is well modeled, we also explore a novel LAMA overlapping penalty and a local region-negative triplet loss in our proposed MLRM method. Comprehensive experiments conducted on five datasets (i.e., Sketchy, QMUL-ChairV2, QMUL-ShoeV2, QMUL-Chair, QMUL-Shoe) demonstrate effectiveness of our method.