The plasmon opens up the possibility to efficiently couple light and matter at subwavelength scales. In general, the plasmon frequency, intensity, and damping are dependent on the carrier density. These dependencies, however, are disadvantageous for stable functionalities of plasmons and render fundamentally a weak intensity at low frequency, especially for the Dirac plasmon (DP) widely studied in graphene. Here we demonstrate a new type of DP, emerging from a Dirac nodal-surface state, which can simultaneously exhibit a density-independent frequency, intensity, and damping. Remarkably, we predict the realization of anomalous DP (ADP) in 1D topological electrides, such as Ba_{3}CrN_{3} and Sr_{3}CrN_{3}, by first-principles calculations. The ADPs in both systems have a density-independent frequency and high intensity, and their frequency can be tuned from terahertz to midinfrared by changing the excitation direction. Furthermore, the intrinsic weak electron-phonon coupling of anionic electrons in electrides affords an added advantage of low-phonon-assisted damping and hence a long lifetime of the ADPs. Our Letter paves the way to developing novel plasmonic and optoelectronic devices by combining topological physics with electride materials.