  We revisit the calculation of the three-loop diagrams for the radiative
neutrino mass generation and consider some relevant constraints on the model
recently proposed by L. Jin {\it et al} [Phys. Lett. B 741 (2015) 163]. We find
that the previous approximation is inappropriate due to the neglect of some
important contributions, and the benchmark point proposed can neither give rise
to enough neutrino masses nor accommodate these additional constraints, such as
the validity of the perturbation theory, the electroweak precision
measurements, and the neutrinoless double beta decays.
