  Weakly interacting massive particle (WIMP) as a dark matter (DM) candidate is
further inspired by recent AMS-02 data, which confirm the excess of positron
fraction observed earlier by PAMELA and Fermi-LAT experiments. Additionally,
the excess of positron+electron flux is still significant in the measurement of
Fermi-LAT. For solving the problems of massive neutrinos and observed excess of
cosmic-ray, we study the model with an inert Higgs doublet (IHD) in the
framework of type-II seesaw model by imposing a $Z_2$ symmetry on the IHD,
where the lightest particle of IHD is the DM candidate and the neutrino masses
originate from the Yukawa couplings of Higgs triplet and leptons. We calculate
the cosmic-ray production in our model by using three kinds of neutrino mass
spectra, which are classified by normal ordering, inverted ordering and
quasi-degeneracy. We find that when the constraints of DM relic density and
comic-ray antiproton spectrum are taken into account, the observed excess of
positron/electron flux could be explained well in normal ordered neutrino mass
spectrum. Moreover, excess of comic-ray neutrinos is implied in our model. We
find that our results on $\langle \sigma v \rangle$ are satisfied with and
close to the upper limit of IceCube analysis. More data from comic-ray
neutrinos could test our model.
