  The nonzero neutrino mass can be a signal for new physics beyond the standard
model. To explain the tiny neutrino mass, we can extend the standard model with
right-handed Majorana neutrinos in a low-scale seesaw mechanism, while the CP
violation effect can be induced due to the CP phase in the interference of
heavy Majorana neutrinos. The existence of heavy Majorana neutrinos may lead to
lepton number violation processes, which can be used as a probe to search for
the signal of heavy Majorana neutrinos. In this paper, we focus on the CP
violation effect related to two generations of heavy Majorana neutrinos for
$15$ GeV $<m_N<$ $70$ GeV in the pair production of W bosons and rare decays.
It is valuable to investigate the Majorana neutrino production signals and the
related CP violation effects in the W boson rare decays at future lepton
colliders.
