Private function evaluation is a task that aims to obtain the output of a function while keeping the function secret. So far its quantum analogue has not yet been articulated. In this study, we initiate the study of quantum private function evaluation, the quantum analogue of classical private function evaluation. We give a formal definition of quantum private function evaluation and present two schemes together with their security proofs. We then give an experimental demonstration of the scheme. Finally we apply quantum private function evaluation to quantum copy protection to illustrate its usage.