  We study the Zee model of neutrino mass in the framework of R-parity
violating supersymmetry. Within the matter contents of the minimal
supersymmetric standard model, any one of the three right-handed sleptons could
be a suitable candidate for the charged-singlet scalar of the Zee model, and
one of the Higgs doublets provides the extra necessary vacuum expectation
value. A combination of one bilinear and two trilinear R-parity-violating
couplings then completes the model. In this framework, we also discuss other
various contributions to neutrino masses and derive the conditions for the
dominance of the contribution from the Zee model, and hence maintain the
successfully Zee mass texture. However, this model within the minimal
supersymmetric standard model is shown to be only marginally feasible. More
general versions of supersymmetrization of the Zee model are also discussed. A
particularly interesting example that has extra Higgs doublets while the
slepton, especially the selectron, keeps the role of the Zee scalar is
illustrated.
