In this paper, we present a system for incrementally reconstructing a dense 3D model of the geometry of an outdoor environment using a single monocular camera attached to a moving vehicle. Dense models provide a rich representation of the environment facilitating higher-level scene understanding, perception, and planning. Our system employs dense depth prediction with a hybrid mapping architecture combining state-of-the-art sparse features and dense fusion-based visual SLAM algorithms within an integrated framework. Our novel contributions include design of hybrid sparse-dense camera tracking and loop closure, and scale estimation improvements in dense depth prediction. We use the motion estimates from the sparse method to overcome the large and variable inter-frame displacement typical of outdoor vehicle scenarios. Our system then registers the live image with the dense model using whole-image alignment. This enables the fusion of the live frame and dense depth prediction into the model. Global consistency and alignment between the sparse and dense models are achieved by applying pose constraints from the sparse method directly within the deformation of the dense model. We provide qualitative and quantitative results for both trajectory estimation and surface reconstruction accuracy, demonstrating competitive performance on the KITTI dataset. Qualitative results of the proposed approach are illustrated in https://youtu.be/Pn2uaVqjskY. Source code for the project is publicly available at the following repository https://github.com/robotvisionmu/DenseMonoSLAM.