Artificial intelligence (AI) based device identification improves the security of the internet of things (IoT), and accelerates the authentication process. However, existing approaches rely on the assumption that we can learn all the classes from the training set, namely, closed-set classification. To overcome the closed-set limitation, we propose a novel open set RF device identification method to classify unseen classes in the testing set. First, we design a specific convolution neural network (CNN) with a short-time Fourier transforming (STFT) preprocessing module, which efficiently recognizes the differences of feature maps learned from various RF device signals. Then to generate a representation of known class bounds, we model the peripheral samples' distribution and revise CNN's output according to the extreme value theory (EVT). Finally, we estimate the probability map of the open-set via the OpenMax function.We conduct experiments on sampled data and voice signal sets, considering various pre-processing schemes, network structures, distance metrics, tail sizes, and openness degrees. The simulation results show the superiority of the proposed method in terms of robustness and accuracy.