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In this work, we propose a novel single-shot and keypoints-based framework for monocular 3D objects detection using only RGB images, called KM3D-Net. We design a fully convolutional model to predict object keypoints, dimension, and orientation, and then combine these estimations with perspective geometry constraints to compute position attribute. Further, we reformulate the geometric constraints as a differentiable version and embed it into the network to reduce running time while maintaining the consistency of model outputs in an end-to-end fashion. Benefiting from this simple structure, we then propose an effective semi-supervised training strategy for the setting where labeled training data is scarce. In this strategy, we enforce a consensus prediction of two shared-weights KM3D-Net for the same unlabeled image under different input augmentation conditions and network regularization. In particular, we unify the coordinate-dependent augmentations as the affine transformation for the differential recovering position of objects and propose a keypoints-dropout module for the network regularization. Our model only requires RGB images without synthetic data, instance segmentation, CAD model, or depth generator. Nevertheless, extensive experiments on the popular KITTI 3D detection dataset indicate that the KM3D-Net surpasses all previous state-of-the-art methods in both efficiency and accuracy by a large margin. And also, to the best of our knowledge, this is the first time that semi-supervised learning is applied in monocular 3D objects detection. We even surpass most of the previous fully supervised methods with only 13\% labeled data on KITTI.