Reaching-and-grasping is a fundamental skill for robotic ma-nipulation, but existing methods usually train models on a specific gripper and cannot be reused on another gripper without retraining. In this paper, we propose a novel method that can learn a unifed policy modelthat can be easily transferred to different dexterous grippers. Our method consists of two stages: a gripper-agnostic policy model that predicts thedisplacements of predefined key points on the gripper, and a gripperspecifc adaptation model that translates these displacements into adjustments for controlling the grippers’ joints.The gripper state and interactions with objects are captured at the finger level using robust geometric representations integrated with a transformer-based network to address variations in gripper morphology and geometry. We evaluateour method on several dexterous grippers and objects of diverse shapes.And the result shows our method signifcantly outperforms the base-line methods. Our method pioneers the transfer of grasp policies acrossdifferent dexterous grippers, and demonstrates the potential of learn-ing generalizable and transferable manipulation skills for various robotichands.