The novel fault diagnosis method of gearbox based on FBEWT and manifold regularization ELM is proposed to obtain excellent fault diagnosis results of gearbox in this paper. A new feature extraction strategy based on Bessel series expansion-based empirical wavelet transform Fourier (FBEWT) is used to capture the key non-stationary features of the vibrational signal of gearbox, and significantly improve the diagnosis ability of gearbox. The ELM with manifold regularization is proposed for fault diagnosis of gearbox. In order to outstand the superiority and stability of the proposed FBEWT and manifold regularization ELM, the balanced dataset and unbalanced dataset, respectively, are used. The experimental results testify that FBEWT-MRELM are more superior and stable than EWT-MRELM, and EWT-ELM regardless of balanced dataset and unbalanced dataset.