  We discuss a two Higgs doublet model with extra $U(1)_X$ gauge symmetry where
lepton specific (type-X) structure for Yukawa interactions is realized by
charge assignment of fields under the $U(1)_X$. Extra charged leptons are
introduced to cancel gauge anomaly associated with extra gauge symmetry. In
addition, we introduce scalar fields as dark matter candidates to which we
assign $Z_2$ odd parity for guaranteeing stability of them. We then analyze
phenomenology of the model such as scalar potential, muon anomalous magnetic
dipole moment, collider physics associated with $Z'$ boson from $U(1)_X$, and
dark matter physics. Carrying out numerical analysis we search for
phenomenologically viable parameter region.
