  We propose a two-Higgs-doublet model in which one Higgs doublet has the same
interactions with fermions as the SM, and another Higgs doublet only has the
$\mu$-$\tau$ LFV interactions. Assuming that the Yukawa matrices are real and
symmetric, we impose various relevant theoretical and experimental constraints,
and find that the excesses of muon $g-2$ and lepton flavour universality in the
$\tau$ decays can be simultaneously explained in the region of small mass
splittings between the heavy CP-even Higgs and the CP-odd Higgs ($m_A > m_H$).
The multi-lepton event searches at the LHC can sizably reduce the mass ranges
of extra Higgses, and $m_H$ is required to be larger than 560 GeV.
