The spectral hardenings of cosmic ray nuclei above ∼ 200 GV followed by softenings around 10 TV, the knee of the all-particle spectrum around PeV energies, as well as the pattern change of the amplitude and phase of the large-scale anisotropies around 100 TeV indicate the complexities of the origin and transportation of Galactic cosmic rays. It has been shown that nearby source(s) are most likely to be the cause of such spectral features of both the spectra and the anisotropies. In this work, we study the anisotropy features of different mass composition (or mass groups) of cosmic rays in this nearby source model. We show that even if the spectral features from the nearby source component is less distinctive compared with the background component from e.g., the population of distant sources, the anisotropy features are more remarkable to be identified. Measurements of the anisotropies of each mass composition (group) of cosmic rays by the space experiments such as DAMPE and HERD and the ground-based experiments such as LHAASO in the near future are expected to be able to critically test this scenario.