The hand-eye calibration and inverse kinematics solution of the 6-degree-of-freedom robot based on visual servo control has always been the core problem in this field. With the application scene becoming more complex, the traditional hand-eye calibration method cannot meet requirements. At the same time, based on the single BP neural network inverse kinematics algorithm, the error tends to be saturated or even larger, which cannot further improve the network performance with the increase of network depth to a certain extent. In order to solve the above problems, the problem of hand-eye calibration and inverse kinematics was integrated into the problem of fitting the mapping relationship between the coordinates of the target image and the joint angles of the 6-degree-of-freedom series robot, and a residual BP neural network algorithm was proposed，the multiple residual network modules were used to deepen the depth of the BP neural network, and the input information of the residual module can be transmitted across layers in the network. It solved the problem that the gradient of the network model was easy to disappear and cannot improve the network performance with the increase of depth. In addition, the space of the inverse kinematics solutions was divided into eight unique regions by the six-degree-of-freedom robot Jacobi equation, and the training data were processed based on this way, the influence of multi-solution of inverse kinematics of multi-degree-of-freedom robot on network learning was avoided, and the accuracy of network training results was improved by two orders of magnitude, and the training speed was increased by two times. Finally, two-dimensional plane grasping and three-dimensional physical grasping experiments were carried out in the REBot-V-6R 6 degree of freedom robot conveyor line sorting system, and the experimental results verified the accuracy of the method. Compared with single-layer BP neural network, three-layer BP neural network and five-layer BP neural network, the training accuracy was improved by four orders of magnitude, two orders of magnitude and five orders of magnitude, respectively, and the testing accuracy was improved by two orders of magnitude，and the computational cost of inverse kinematics was saved and the accuracy was improved by one order of magnitude.