  Neutrino masses and their mixing are studied in detail in the framework of a
supersymmetric standard model with bilinear R-parity violation. In this
scenario, the mixing matrix among the neutrinos is in a restrictive form. We
find that only the small angle MSW solution is allowed for the solar neutrino
problem when the results of the CHOOZ experiment are combined with the mass
squared difference and mixing angle suggested by the atmospheric neutrino data.
Collider signals of this scenario are also discussed.
