Due to the symmetry of the rolling bearing structure and the rotating operation mode, it will cause the coupling modulation phenomenon when it is damaged in multiple places at the same time, which makes it difficult to accurately identify all kinds of faults. For such problems, a compound fault diagnosis method based on adaptive chirp mode decomposition (ACMD), Gini index fusion and long short-term memory (LSTM) neural network optimized by Aquila Optimizer (AO) is proposed. Firstly, a series of IMF components are obtained by decomposing the vibration signal by means of ACMD, and the required components are selected by using the correlation coefficient method. Then, the Gini index of the square envelope (GISE) and the Gini index of the square envelope spectrum (GISES) of each component are calculated, respectively, and they are fused to construct a highly dimensional feature matrix. Then, with the aim of solving the problem of difficult selection of LSTM hyperparameters, the AO-LSTM model is constructed. Finally, the feature matrix is divided into a training set and a test set. The training set is input into the model for training, and then the training network is used to predict the test set, and outputs diagnostic results. The simulation and experimental results show that the proposed method can achieve higher accuracy and stronger robustness, compared with the existing intelligent diagnosis methods for bearing compound faults.