Data-efficient domain adaptation with only a few labelled data is desired for many robotic applications, e.g., in grasping detection, the inference skill learned from a grasping dataset is not universal enough to directly apply on various other daily/industrial applications. This paper presents an approach enabling the easy domain adaptation through a novel grasping detection network with confidence-driven semi-supervised learning, where these two components deeply interact with each other. The proposed grasping detection network specially provides a prediction uncertainty estimation mechanism by leveraging on Feature Pyramid Network (FPN), and the mean-teacher semi-supervised learning utilizes such uncertainty information to emphasizing the consistency loss only for those unlabelled data with high confidence, which we referred it as the confidence-driven mean teacher. This approach largely prevents the student model to learn the incorrect/harmful information from the consistency loss, which speeds up the learning progress and improves the model accuracy. Our results show that the proposed network can achieve high success rate on the Cornell grasping dataset, and for domain adaptation with very limited data, the confidence-driven mean teacher outperforms the original mean teacher and direct training by more than 10% in evaluation loss especially for avoiding the overfitting and model diverging.