It is a very difficult work to detect gear fault under non-stationary condition. Due to the complexity of gear vibration signals, it is difficult to extract fault features and diagnose faults. In order to solve these problems, based on radial basis function (RBF) neural network, this paper proposes a gear fault diagnosis method, which is CIHDRFD. In the CIHDRFD method, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is used firstly to decompose the original vibration signal into multiple inherent modal functions (IMFs), and by calculating its information entropy (IE), the 4 IMFs with the smallest IE are selected as the characteristic IMF. Then, the Hilbert transform (HT) is used to process the feature IMF and the Hilbert envelope spectrum is obtained. The Hilbert envelope spectrum is used to construct the fault feature vector. Finally, the improved double RBF neural network is used for fault diagnosis. The effectiveness of the CIHDRFD method is verified by building a gear failure detection platform. Experimental results show that the CIHDRFD method is suitable for gear fault diagnosis. When the speed fluctuation is 3%, the diagnostic accuracy and diagnosis time of the CIHDRFD method are 98.21% and 74.53s, respectively.