Neural implicit representations have recently been demonstrated in many fields including Simultaneous Localization And Mapping (SLAM). Current neural SLAM can achieve ideal results in reconstructing bounded scenes, but this relies on the input of RGB-D images. Neural-based SLAM based only on RGB images is unable to reconstruct the scale of the scene accurately, and it also suffers from scale drift due to errors accumulated during tracking. To overcome these limitations, we present MoD-SLAM, a monocular dense mapping method that allows global pose optimization and 3D reconstruction in real-time in unbounded scenes. Optimizing scene reconstruction by monocular depth estimation and using loop closure detection to update camera pose enable detailed and precise reconstruction on large scenes. Compared to previous work, our approach is more robust, scalable and versatile. Our experiments demonstrate that MoD-SLAM has more excellent mapping performance than prior neural SLAM methods, especially in large borderless scenes.