Rotating machinery is a primary element of mechanical equipment, and thus fault diagnosis of its key components is very important to improve the reliability and safety of modern industrial systems. The key point to diagnose the faults of these components is to extract effectively the hidden fault information. However, the actual vibration signals of rotating machinery have nonlinear and non-stationary characteristics, so traditional signal decomposition methods are unable to extract the frequency components accurately, leading to spectrum overlap of the decomposed sub-signals. Therefore, a rotating machinery fault diagnosis approach based on Fourier transform multi-filter decomposition (FTMFD), fuzzy entropy (FE), joint mutual information maximization (JMIM), and a light gradient boosting machine (LightGBM), is proposed in this paper. FTMFD is used to extract the frequency domain information of the raw vibration signals, whereas FE is used to calculate and extract the fault information of the decomposed sub-signals. Then feature selection is carried out by using JMIM to reduce the influence of redundant features on data analysis and classification accuracy. Furthermore, LightGBM is used to rank the candidate features and outputs the fault diagnosis result. Experimental results from two real datasets show that the proposed method achieves higher accuracy with fewer features than some existing methods for fault recognition. Various working conditions are also considered and verified.