It is a challenge for bearing fault diagnosis to effectively reduce the dimension of high dimensional data and improve the accuracy of fault identification. To address this issue, a novel fault diagnosis method based on locally generalized preserving projection (LGPP) and flexible grey wolf optimizer-based extreme learning machine (FGWO-ELM) is proposed in this paper. Firstly, the high dimensional features are obtained from the time–frequency domain of the signal. Secondly, a novel LGPP algorithm is proposed to reduce the dimension of high dimensional features more effectively. The algorithm uses a generalized discriminant matrix to calculate the degree similarity between data, rather than a simple Euclidean distance, so as to obtain sensitive features with better discrimination. Thirdly, a FGWO algorithm is proposed and used to optimize the parameters of ELM to improve the fault recognition rate. Finally, the effectiveness of the proposed fault diagnosis method is verified by two bearing experiments. Experimental results show that compared with other methods, the proposed method not only has the better dimension reduction ability, but also has higher diagnostic accuracy.