When computer vision technique is used in robotics, robotic hand-eye calibration is a very important research task. Many algorithms have been proposed for hand-eye calibration. Based on these algorithms, we introduce a new hand-eye calibration algorithm in this paper, which employs the screw motion theory to establish a hand-eye matrix equation by using quaternion and gets a simultaneous result for rotation and translation by solving linear equations. The algorithm proposed in this paper has high and stable computational efficiency without non-linear minimization and can be understood easily. Both simulations and real experiments show the superiority of our algorithm over the comparative algorithms.