Nowadays, industrial robots are increasingly widely used, and robots that integrate visual systems can efficiently perform a variety of tasks. The core of the hand-eye fusion system is to establish the transformation relationship between the robot and the visual system through hand-eye calibration. Although previous studies have proposed closed solutions and optimization methods for the hand-eye calibration equation through a variety of mathematical tools, this study proposes a two-step solution method based on dual quaternions to address the error transmission and singularity problems in the two-step method. By using the properties of the dual matrix and dual quaternion, the quaternion decoupling principle is transferred to the dual quaternion domain, and the two-step solution based on the dual quaternion is realized. The closed solution and singularity judgment conditions are derived; the translation vector solution equation is reconstructed, and the error transmission path is optimized. Compared with existing methods, including the two-step method based on quaternions and the one-step method based on dual quaternions, this method shows lower errors in both rotation and translation solutions. By designing an Eye-in-hand experiment platform and combining it with a high-precision visual measurement system, the feasibility and robustness of this method are verified, and it has the advantage of low error. Experiment results show that this method can improve the hand-eye calibration accuracy to a rotation error of 0.1994° and a translation error of 1.1126 mm.