In this paper, we focus on how to control the robot end-effector to track an object, meanwhile, to approach it with a suitable posture for grasping. We named it "Approaching Visual Servoing". A proposed hand & eye-vergence dual control system is used to perform Approaching Visual Servoing, aiming at quick eye-tracking and stable hand servoing and approaching. This idea stems from hammerhead shark whose 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. Moreover, a 3-D pose tracking method that combines "1-Step GA (genetic algorithm)" and hand-motion feedforword compensation is proposed. Our approach differs from known tracking methods using optimization based on Taylor expansion, for it allows the proposed method not to be annoyed by how to sneak out of local minima. A convergence in time domain - whether the 3-D pose tracking error decrease to zero in a successively input images by video rate -, is discussed and verified through Lyapunov method. Both Lyapunouv-stable pose tracking and Approaching Visual Servoing are confirmed by experiments using a 7-link manipulator installed with two mobile cameras.