Aiming at the hand-eye calibration problem related to Eye-in-Hand vision and robot body of picking board, an optimization problem based on AX=ZB calibration equation was proposed. Firstly, the camera was driven by the robot to observe the calibration plate in multiple positions, and multiple calibration equations were obtained. One calibration equation AX=ZB was established by collecting data once. Kronecker product algorithm and the least square method were used to solve the calibration rotation matrix, and then the translation vector was solved according to rotation matrix and the least square method. In order to avoid the error transfer problem, the Jacobian matrix, the error function and Levenberg-Marquardt algorithm were established to optimize the attitude and position of the initial value simultaneously. Then, a simulation experiment platform was built in the ROS system, and the validity of calibration results was verified by the 3D visualization tool Rviz. The accuracy analysis of the calibration results showed that the accuracy of the new calibration method was increased by 30% on average compared with the traditional calibration method under different noise levels, and the accuracy of the new calibration method was increased by 31.1% on average compared with the traditional calibration method under different noise levels. Finally, the results of the grab test showed that the accuracy of the visual system was 39.2% higher than that of the transmission calibration method, and the success rate of the grab was 96.2%.