The present invention discloses a fault diagnosis method under a convergence trend of a center frequency, including: (1) acquiring a dynamic signal x(t) of a rotary machine equipment; (2) setting initial decomposition parameters of a variational model; (3) decomposing the dynamic signal x(t) by using the variational model with the set initial decomposition parameters, and traversing a signal analysis band and performing iterative decomposition on the dynamic signal x(t) under the guidance of a convergence trend of a center frequency, to obtain optimized modals {m1 . . . mn . . . mN} and corresponding center frequencies {ω1 . . . ωn . . . ωN}; (4) searching a fault related modal mI, guiding parameter optimization by using a center frequency ωI of the fault related modal mI, and retrieving an optimal target component mI including fault information; and (5) performing envelopment analysis on the optimal target component mI, and diagnosing the rotary machine equipment according to an envelope spectrum.