To address the problems existed in the process of tacho-less order tracking (TLOT) based fault diagnosis, such as the error accumulation effect of harmonic components extraction and the difficulty of accurate instantaneous phase estimation, a speed-varying fault diagnosis method for the accessory transmission system based on adaptive harmonic components extraction is proposed. Firstly, the vibration signal is low-pass filtered and down-sampled for computation speed acceleration. Harmonic components are subsequently extracted by the adaptive symplectic geometry mode decomposition (ASGMD) based on the autocorrelation average periods. Secondly, surrogate data test is applied for pseudo components identification. Therefore, interferences induced by background noise can be filtered out adaptively. Finally, Hilbert transform is applied to obtain the instantaneous phase of the decomposed fundamental harmonic component. The TLOT is conducted to realize fault diagnosis for rotating machinery equipment under speed-varying conditions. The simulation analysis and an experiment from a Safran aero-engine during the frequency sweep test exhibit that the proposed method has a relative error of 0. 059% in TLOT. This result is better than those of conventional approaches. The bright prospect is evaluated in industrial application.