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The neutrino and Higgs sectors in the $\mbox{SU(2)}_1 \times \mbox{SU(2)}_2\times \mbox{U(1)}_Y $ model with lepton-flavor non-universality are discussed.We show that active neutrinos can get Majorana masses from radiativecorrections, after adding only new singly charged Higgs bosons. The mechanismfor generation of neutrino masses is the same as in the Zee models. This alsogives a hint to solving the dark matter problem based on similar ways discussedrecently in many radiative neutrino mass models with dark matter. Except theactive neutrinos, the appearance of singly charged Higgs bosons and dark matterdoes not affect significantly the physical spectrum of all particles in theoriginal model. We indicate this point by investigating the Higgs sector inboth cases before and after singly charged scalars are added into it. Manyinteresting properties of physical Higgs bosons, which were not shownpreviously, are explored. In particular, the mass matrices of charged andCP-odd Higgs fields are proportional to the coefficient of triple Higgscoupling $\mu$. The mass eigenstates and eigenvalues in the CP-even Higgssector are also presented. All couplings of the SM-like Higgs boson to normalfermions and gauge bosons are different from the SM predictions by a factor$c_h$, which must satisfy the recent global fit of experimental data, namely$0.995<|c_h|<1$. We have analyzed a more general diagonalization of gauge bosonmass matrices, then we show that the ratio of the tangents of the $W-W'$ and$Z-Z'$ mixing angles is exactly the cosine of the Weinberg angle, implying thatnumber of parameters is reduced by 1. Signals of new physics from decays of newheavy fermions and Higgs bosons at LHC and constraints of their masses are alsodiscussed.

Probing neutrino and Higgs sectors in $SU(2)_1 \times SU(2)_2 \times U(1)_Y$ model with lepton-flavor non-universality