In order to overcome the restrictions of traditional hand-eye methods for determining hand-eye correspondence and robot-world orientation with a calibration reference, an improved hand-eye calibration approach without a calibration reference is proposed based on second-order cone programming. A relevant experimental system is established for its validation. First, a structure-from-motion approach is used to recover the camera motion matrix up to scaling. Then, the rotation and translation matrix in the calibration equation is parameterized by dual quaternion theory. Finally, the second-order cone programming method is used to simultaneously determine the optimal solution for the scale factor of the camera motion matrix, the robot-world calibration and the hand-eye calibration. Both the simulation and experimental results indicate that, for the calibration precision, the relative error of rotation is 3.998% and the relative error of translation is 0.117% in the absence of a calibration reference as a benchmark. Compared with other calibration methods, the proposed method can effectively improve the accuracy of robot-world calibration and hand-eye calibration without a reference, and extend the range of applications of the hand-eye calibration method.