The vision system is a crucial technology for realizing the automation and intelligence of industrial robots, and the accuracy of hand–eye calibration is crucial in determining the relationship between the camera and robot end. Parallel robots are widely used in automated assembly due to their high positioning accuracy and large carrying capacity, but traditional hand–eye calibration methods may not be applicable due to their limited motion range and resulting accuracy problems. To address this issue, we propose using a pose, nonlinear mapping estimation method to solve the hand–eye calibration problem and have constructed a 1-D pose estimation convolutional neural network (PECNN) with excellent performance, through experiments and discussions. The PECNN achieves an end-to-end mapping of the variation of the target object pose to the variation of the robot end pose. Our experiments have shown that the proposed hand–eye calibration method has high accuracy and can be applied to the automated assembly tasks of vision-guided parallel robots. Moreover, the method is also applicable to most parallel robots and tandem robots.