A novel detection method based on multivariate extended variational mode decomposition-based time–frequency images and incremental RVM algorithm (MEVMDTFI–IRVM) is presented for fault detection of gearbox. The time–frequency images are constructed by multivariate extended variational mode decomposition. Compared with single-variable modal decomposition method, multivariate extended variational mode decomposition not only has an accurate mathematical framework, but also has good robustness to non-stationary multi-channel signals with low signal-to-noise ratio. The incremental RVM algorithm is presented for fault detection of gearbox based on the time–frequency images constructed by multivariate extended variational mode decomposition. The testing results demonstrate that the detection results of MEVMDTFI–IRVM for gearbox are stable, in addition, the detection results of MEVMDTFI–IRVM for gearbox are better than those of variational mode decomposition-based time–frequency images and incremental RVM algorithm (VMDTFI–IRVM), variational mode decomposition–RVM algorithm (VMD–RVM), and traditional RVM algorithm.