  We present the radiative corrections to neutrino masses in a minimal
supersymmetric extension of the standard model with local $U(1)_{B-L}$
symmetry. At tree level, three tiny active neutrinos and two nearly massless
sterile neutrinos can be obtained through the seesaw mechanism. Considering the
one-loop corrections to the neutrino masses, the numerical results indicate
that two sterile neutrinos obtain ${\rm KeV}$ masses and the small
active-sterile neutrino mixing angles. The lighter sterile neutrino is a very
interesting dark matter candidate in cosmology. Meanwhile the active neutrinos
mixing angles and mass squared differences agree with present experimental
data.
