  The model proposed by A. Zee (1986) and K.S. Babu (1988) is a simple
radiative seesaw model, in which tiny neutrino masses are generated at the
two-loop level. We investigate a supersymmetric extension of the Zee-Babu model
under R-parity conservation. The lightest superpartner particle can then be a
dark matter candidate. We find that the neutrino data can be reproduced with
satisfying current data from lepton flavour violation even in the scenario
where not all the superpartner particles are heavy. Phenomenology at the Large
Hadron Collider is also discussed.
