3D single object tracking plays a crucial role in computer vision. Mainstream methods mainly rely on point clouds to achieve geometry matching between target template and search area. However, textureless and incomplete point clouds make it difficult for single-modal trackers to distinguish objects with similar structures. To overcome the limitations of geometry matching, we propose a Multi-modal Multi-level Fusion Tracker (MMF-Track), which exploits the image texture and geometry characteristic of point clouds to track 3D target. Specifically, we first propose a Space Alignment Module (SAM) to align RGB images with point clouds in 3D space, which is the prerequisite for constructing inter-modal associations. Then, in feature interaction level, we design a Feature Interaction Module (FIM) based on dual-stream structure, which enhances intra-modal features in parallel and constructs inter-modal semantic associations. Meanwhile, in order to refine each modal feature, we introduce a Coarse-to-Fine Interaction Module (CFIM) to realize the hierarchical feature interaction at different scales. Finally, in similarity fusion level, we propose a Similarity Fusion Module (SFM) to aggregate geometry and texture clues from the target. Experiments show that our method achieves state-of-the-art performance on KITTI (39% Success and 42% Precision gains against previous multi-modal method) and is also competitive on NuScenes.