Environment perception, including object detection and distance estimation, is one of the most crucial tasks for autonomous driving. Many attentions have been paid on the object detection task, but distance estimation only arouse few interests in the computer vision community. Observing that the traditional inverse perspective mapping algorithm performs poorly for objects far away from the camera or on the curved road, in this paper, we address the challenging distance estimation problem by developing the first end-toend learning-based model to directly predict distances for given objects in the images. Besides the introduction of a learning-based base model, we further design an enhanced model with a keypoint regressor, where a projection loss is defined to enforce a better distance estimation, especially for objects close to the camera. To facilitate the research on this task, we construct the extented KITTI and nuScenes (mini) object detection datasets with a distance for each object. Our experiments demonstrate that our proposed methods outperform alternative approaches (e.g., the traditional IPM, SVR) on object-specific distance estimation, particularly for the challenging cases that objects are on a curved road. Moreover, the performance margin implies the effectiveness of our enhanced method.