  We propose a model for neutrino mass generation based on both the tree-level
seesaw mechanism with a single right-handed neutrino and one-loop radiative
effects in a non-supersymmetric framework. The generated mass matrix is
composed of two parts which have the same texture and produce neutrino mass
eigenvalues and mixing suitable for the explanation of neutrino oscillations.
The model has a good CDM candidate which contributes to the radiative neutrino
mass generation. The stability of the CDM candidate is ensured by $Z_2$ which
is the residual symmetry of a spontaneously broken U(1)$^\prime$. We discuss
the values of $U_{e3}$ and also estimate the masses of the relevant fields to
realize an appropriate abundance of the CDM.
