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Monocular visual odometry (VO) is an important task in robotics and computer vision. Thus far, how to build accurate and robust monocular VO systems that can work well in diverse scenarios remains largely unsolved. In this paper, we propose a framework to exploit monocular depth estimation for improving VO. The core of our framework is a monocular depth estimation module with a strong generalization capability for diverse scenes. It consists of two separate working modes to assist the localization and mapping. With a single monocular image input, the depth estimation module predicts a relative depth to help the localization module on improving the accuracy. With a sparse depth map and an RGB image input, the depth estimation module can generate accurate scale-consistent depth for dense mapping. Compared with current learning-based VO methods, our method demonstrates a stronger generalization ability to diverse scenes. More significantly, our framework is able to boost the performances of existing geometry-based VO methods by a large margin.