RF fingerprints can be used for device identification and network access authentication. An RF fingerprint extraction and device identification algorithm based on multi-scale fractal features and APWOA-LSSVM is proposed. First, a Hilbert transform is performed on the original RF signal, and differential operations are performed on the I/Q signal. Then, the variational modal decomposition is performed on the differentially processed I/Q signals separately to obtain a number of band-limited Intrinsic Modal Function (IMF) components. The fractal box dimension of each IMF component is calculated separately as the first dimensional RF fingerprint. The multi-fractal spectrum of the original RF signal is further computed by Multi-fractal Detrended Fluctuation Analysis (MFDFA) as the second dimensional RF fingerprint. The RF fingerprint feature vector consists of a combination of the first and second dimensional RF fingerprints and is used to train the LSSVM model. Since the penalty factor and kernel parameter width directly affect the recognition accuracy and generalization ability of the LSSVM model, APWOA is used to optimize the hyperparameters of the LSSVM model. Finally, the LSSVM model is constructed using the optimal hyperparameters and the performance of the model is verified on a test dataset. The experimental results show that the proposed model achieves an average recognition accuracy of 99.13% for 16 Bluetooth devices. Multi-scale fractal features consisting of fractal box dimensions and multiple fractal dimensions are more beneficial in the recognition of wireless devices as compared to single features. In addition, the proposed model possesses superior recognition capabilities when compared to classical machine learning algorithms.