  We study the models with the Majorana neutrino masses generated radiatively
by two-loop diagrams due to the Yukawa $\rho \bar \ell_R^c \ell_R$ and
effective $\rho^{\pm\pm} W^\mp W^\mp$ couplings along with a scalar triplet
$\Delta$, where $\rho$ is a doubly charged singlet scalar, $\ell_R$ the charged
lepton and $W$ the charged gauge boson. A generic feature in these types of
models is that the neutrino mass spectrum has to be a normal hierarchy.
Furthermore, by using the neutrino oscillation data and comparing with the
global fitting result in the literature, we find a unique neutrino mass matrix
and predict the Dirac and two Majorana CP phases to be $1.40\pi$, $1.11\pi$ and
$1.47\pi$, respectively. We also discuss the model parameters constrained by
the lepton flavor violating processes and electroweak oblique parameters. In
addition, we show that the rate of the neutrinoless double beta decay
$(0\nu\beta\beta)$ can be as large as the current experimental bound as it is
dominated by the short-range contribution at tree level, whereas the
traditional long-range one is negligible.
