  Motivated by the very recent cosmic-ray electron+positron excess observed by
DAMPE collaboration, we investigate a Dirac fermion dark matter (DM) in the
gauged $L_e - L_\mu$ model. DM interacts with the electron and muon via the
$U(1)_{e-\mu}$ gauge boson $Z^{'}$. The model can explain the DAMPE data well.
Although a non-zero DM-nucleon cross section is only generated at one loop
level and there is a partial cancellation between $Z^{'}ee$ and $Z^{'}\mu\mu$
couplings, we find that a large portion of $Z^{'}$ mass is ruled out from
direct DM detection limit leaving the allowed $Z^{'}$ mass to be close to two
times of the DM mass. Implications for $pp \to Z^{'} \to 2\ell$ and $pp \to
2\ell + Z^{'}$ , and muon $g-2$ anomaly are also studied.
