With the rapid development of communication technology and the advancement of the Internet of Things revolution, the application range and scenarios of wireless communication devices are expanding increasingly. The classification and authentication of device identities, as a key link to realize large-scale applications, are core issues to ensure the security of wireless networks. Aimed at the problem of low radio frequency (RF) fingerprint classification and recognition rate among identical wireless communication devices, this study proposes an improved Convolutional Neural Network-Gated Recurrent Unit (CNN-GRU) RF fingerprint classification and recognition method based on a comb filter preprocessing technique. Firstly, an RF fingerprint feature extraction method based on comb filter is proposed, which amplifies RF fingerprint features at fixed frequency positions to enhance feature robustness. Secondly, based on the traditional CNN-GRU network, the original one-dimensional feature extraction module is elevated to a two-dimensional module that can extract complex signal features after comb filter preprocessing. Finally, the complex signals processed by the comb filter are input into the improved network model for feature extraction and training to calculate the recognition rate. Simulation experiments are conducted with WiFi signals measured in an anechoic Line-Of-Sight (LOS) environment as the objects to be recognized. The results show that using complex signals obtained from the comb filter algorithm as input, under the improved CNN-GRU network, the recognition rate of simulation data can reach 100%, and the recognition rate of measured data reaches 93%. The proposal of this algorithm is of great significance in improving the security and management efficiency of IoT devices.