  Weyl semimetals are one kind of three-dimensional gapless semimetal with
nontrivial topology in the momentum space. The chiral anomaly in Weyl
semimetals manifests as a charge imbalance between the Weyl nodes of opposite
chiralities induced by parallel electric and magnetic fields. We investigate
the chiral anomaly effect on the plasmon mode in both intrinsic and doped Weyl
semimetals within the random phase approximation. We prove that the chiral
anomaly gives rise to a different plasmon mode in intrinsic Weyl semimetals. We
also find the chiral anomaly leads to some exotic properties in the plasmon
dispersion in doped Weyl semimetals. Consequently, the unconventional plasmon
mode acts as a signature of the chiral anomaly in Weyl semimetals, by which the
spectrum of plasmon provides a proper way to detect the Lifshitz transition.
