Calibration between robots and cameras is critical in automated robot vision systems. However, conventional manually conducted image-based calibration techniques are often limited by their accuracy sensitivity and poor adaptability to dynamic or unstructured environments. These approaches present challenges for ease of calibration and automatic deployment while being susceptible to rigid assumptions that degrade their performance. To close these limitations, this study proposes a data-efficient vision-driven approach for fast, accurate, and robust hand–eye camera calibration, and it aims to maximise the efficiency of robots in obtaining hand–eye calibration images without compromising accuracy. By analysing the previously captured images, the minimisation of the residual Jacobian matrix is utilised to predict the next optimal pose for robot calibration. A method to adjust the camera poses in dynamic environments is proposed to achieve efficient and robust hand–eye calibration. It requires fewer images, reduces dependence on manual expertise, and ensures repeatability. The proposed method is tested using experiments with actual industrial robots. The results demonstrate that our NBV strategy reduces rotational error by 8.8%, translational error by 26.4%, and the number of sampling frames by 25% compared to artificial sampling. The experimental results show that the average prediction time per frame is 3.26 seconds.