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Robot grasp dataset is the basis of designing the robot's grasp generation model. Compared with the building grasp dataset for Low-DOF grippers, it is harder for High-DOF dexterous robot hand. Most current datasets meet the needs of generating stable grasps, but they are not suitable for dexterous hands to complete human-like functional grasp, such as grasp the handle of a cup or pressing the button of a flashlight, so as to enable robots to complete subsequent functional manipulation action autonomously, and there is no dataset with functional grasp pose annotations at present. This paper develops a unique Cost-Effective Real-Simulation Annotation System by leveraging natural hand's actions. The system is able to capture a functional grasp of a dexterous hand in a simulated environment assisted by human demonstration in real world. By using this system, dexterous grasp data can be collected efficiently as well as cost-effective. Finally, we construct the first dexterous functional grasp dataset with rich pose annotations. A Functional Grasp Synthesis Model is also provided to validate the effectiveness of the proposed system and dataset. Our project page is: https://hjlllll.github.io/DFG/.