  We consider a simple extension of the Standard Model with flavor-dependent
$U(1)'$, that has been proposed to explain some of $B$-meson anomalies recently
reported at LHCb. The $U(1)'$ charge is chosen as a linear combination of
anomaly-free $B_3-L_3$ and $L_\mu-L_\tau$. In this model, the flavor structure
in the SM is restricted due to flavor-dependent $U(1)'$ charges, in particular,
quark mixings are induced by a small vacuum expectation value of the extra
Higgs doublet. As a result, it is natural to get sizable flavor-violating
Yukawa couplings of heavy Higgs bosons involving the bottom quark. In this
article, we focus on the phenomenology of the Higgs sector of the model
including extra Higgs doublet and singlet scalars. We impose various bounds on
the extended Higgs sector from Higgs and electroweak precision data, $B$-meson
mixings and decays as well as unitarity and stability bounds, then discuss the
productions and decays of heavy Higgs bosons at the LHC.
