  The existence of Majorana neutrinos must lead to lepton-number violating
processes, and the Majorana nature of neutrinos can only be experimentally
verified via lepton-number violating processes. We propose a new approach to
search for Majorana neutrinos at future electron-positron colliders by
exploiting this feature. We investigate the $\Delta L = 2$ like-sign dilepton
production and find that lepton colliders with different center-of-mass
energies have comparative advantages in resonant production of a Majorana
neutrino in either light neutrino mass range or heavy mass range. At the future
Circular Electron-Positron Collider (CEPC), with 250 GeV center-of-mass energy
and 5 ab$^{-1}$ integrated luminosity, we find that there could be more
significant sensitivity for resonant production of a Majorana neutrino in the
mass range of 5-80 GeV than previous results at LEP2 or LHC. At the 1 TeV ILC
with 1 ab$^{-1}$ integrated luminosity, it has better sensitivity than the
similar process at LHC while the neutrino mass is larger than 250 GeV.
