Perfect optical vortex beam (POVB) is a specific kind of vortex beam with radial intensity distribution and radius both independent of the orbital angular momentum (OAM) states, which has been applied in optical manipulation, optical communication, laser material processing and so on. The detection of OAM states of POVB is critical and challenges remain. A diffractive optical neural network (DNN) has been constructed based on the parallel gradient descent algorithm, and the recognition of the POVB with OAM order ranging from-50 to +50 has been realized experimentally. In this process, the diffraction conversion efficiency can reach up to 58%. This work provides a new method for OAM detection of POVB and shows great potential in various POVB-based applications.