In this paper, we propose a new two-way visual servoing method, named as hand & eye-vergence visual servoing. This idea stems from animal's evolution history, predator have evolved their eye positions to be at the front face and their eyes turn to gaze at the target prey to be suited to triangulation, enhancing the ability to measure precisely the distance to the prey for catching it. This animal's visual tracking includes motion control by visual servoing and triangular eye vergence. Our proposed method includes two loops: an outer loop for conventional visual servoing that direct a manipulator toward a target object and an inner loop for active motion of binocular camera for accurate and broad observation of the target object. The effectiveness of the hand & eye-vergence visual servoing is evaluated through simulations incorporated with actual dynamics of 7-DoF robot on the view points of how the new idea improved the stability in visual servoing dynamics and the accuracy of hand pose.