To assist or replace human beings in completing various tasks, research on the functional grasp synthesis of dexterous hands with high degree-of-freedom (DoF) is necessary and challenging. The dexterous functional grasp requires not only that the grasp is stable but more importantly facilitates the functional manipulation after grasping. Such work still relies on manual annotation when collecting data. To this end, we propose a category-level multi-fingered functional grasp transfer framework, in which we only need to label the hand-object contact relationship on functional parts of one object, and then transfer the contact information through the dense correspondence of functional parts between objects, so as to achieve the functional grasp synthesis for new objects based on the transferred hand-object contact information. We verify this method on three categories of representative objects through simulation experiments and achieve successful functional grasps by labeling only one instance in each category.