  In the light of the $e^{+}+e^{-}$ excess observed by DAMPE experiment, we
propose an anomaly-free radiative seesaw model with an alternative leptophilic
$U(1)_X$ gauge symmetry. In the model, only right-handed leptons are charged
under $U(1)_X$ symmetry. The tiny Dirac neutrino masses are generated at
one-loop level and charged leptons acquire masses though the type-I seesaw-like
mechanism with heavy intermediate fermions. In order to cancel the anomaly,
irrational $U(1)_{X}$ charge numbers are assigned to some new particles. After
the spontaneous breaking of $U(1)_{X}$ symmetry, the dark $Z_{2}$ symmetry
could appear as a residual symmetry such that the stability of inert particles
with irrational charge numbers are guaranteed, naturally leading to stable DM
candidates. We show that the Dirac fermion DM contained in the model can
explain the DAMPE excess. Meanwhile, experimental constraints from DM relic
density, direct detection, LEP and anomalous magnetic moments are satisfied.
