Absorption lines of atmospheric vapor commonly appear in terahertz (THz) spectra measured in a humid air environment. However, these effects are generally undesirable because they may mask critical spectroscopic information. Here, a self-adaptive method is demonstrated for effectively identifying and eliminating atmospheric vapor noise from THz spectra of an all-fiber THz system with the Hilbert-Huang transform. The THz signal was decomposed into eight components in different time scales called the intrinsic mode functions and the interference of atmospheric vapor was accurately isolated. A series of experiments confirmed the effectiveness and strong self-adaptiveness of the proposed system in vapor noise elimination.