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In this paper, we introduce SLAM3R, a novel and effective monocular RGB SLAM system for real-time and high-quality dense 3D reconstruction. SLAM3R provides an end-to-end solution by seamlessly integrating local 3D reconstruction and global coordinate registration through feed-forward neural networks. Given a video input, the system first converts it into overlapping clips using a sliding window mechanism. Unlike traditional pose optimization-based methods, SLAM3R directly regresses 3D pointmaps from RGB images and then progressively aligns and deforms these local pointmaps to create a globally consistent scene reconstruction - all without explicitly solving any camera parameters. Experiments across datasets consistently show that SLAM3R achieves state-of-the-art reconstruction accuracy and completeness while maintaining real-time performance at 20+ FPS. Upon acceptance, we will release our code to support further research.