  Inspired by the peak structure observed by recent DAMPE experiment in
$e^+e^-$ cosmic-ray spectrum, we consider a scalar dark matter (DM) model with
gauged $U(1)_{L_e-L_\mu}$ symmetry, which is the most economical anomaly-free
theory to potentially explain the peak by DM annihilation in nearby subhalo. We
utilize the process $\chi \chi \to Z^\prime Z^\prime \to l \bar{l} l^\prime
\bar{l}^\prime$, where $\chi$, $Z^\prime$, $l^{(\prime)}$ denote the scalar DM,
the new gauge boson and $l^{(\prime)} =e, \mu$, respectively, to generate the
$e^+e^-$ spectrum. By fitting the predicted spectrum to the experimental data,
we obtain the favored DM mass range $m_\chi \simeq 3060^{+80}_{-100} \, {\rm
GeV}$ and $\Delta m \equiv m_\chi - m_{Z^\prime} \lesssim 14 \, {\rm GeV}$ at
$68\%$ Confidence Level (C.L.). Furthermore, we determine the parameter space
of the model which can explain the peak and meanwhile satisfy the constraints
from DM relic abundance, DM direct detection and the collider bounds. We
conclude that the model we consider can account for the peak, although there
exists a tension with the constraints from the LEP-II bound on $m_{Z^\prime}$
arising from the cross section measurement of $e^+e^- \to Z^{\prime\ast} \to
e^+ e^-$.
