We discuss the parity-violating left–right asymmetries (LRAs) in Möller scattering at the International Linear Collider (ILC) induced by doubly charged Higgs bosons in models with SU(2)L triplet and singlet scalar bosons, which couple to the left- and right-handed charged leptons, respectively. These bosons are important in scenarios for the generation of the neutrino mass. We demonstrate that the contributions to the LRAs from the triplet and singlet bosons are opposite to each other. In particular, we show that the doubly charged Higgs boson from the singlet scalar can be tested at the ILC by using the resonance effect.