  Left-Right symmetric model (LRSM) has been an attractive extension of the
Standard Model (SM) which can address the origin of parity violation in the SM
electroweak (EW) interactions, generate tiny neutrino masses, accommodate dark
matter (DM) candidates and provide a natural framework for baryogenesis through
leptogenesis. In this work we utilize the minimal LRSM to study the recently
reported DAMPE results of cosmic $e^+e^-$ spectrum which exhibits a tentative
peak around 1.4 TeV, while satisfying the current neutrino data. We propose to
explain the DAMPE peak with a complex scalar DM $\chi$ in two scenarios: 1)
$\chi\chi^* \to H_1^{++}H_1^{--} \to \ell_i^+\ell_i^+\ell_j^-\ell_j^-$; 2)
$\chi\chi^* \to H_{k}^{++}H_{k}^{--} \to \ell_i^+\ell_i^+\ell_j^-\ell_j^-$
accompanied by $\chi\chi^* \to H_1^+ H_1^- \to \ell_i^+ \nu_{\ell_i} \ell_j^-
\nu_{\ell_j}$ with $\ell_{i,j}=e,\mu,\tau$ and $k=1,2$. We fit the theoretical
prediction on $e^+e^-$ spectrum to relevant experimental data to determine the
scalar mass spectrum favored by the DAMPE excess. We also consider various
constraints from theoretical principles, collider experiments as well as DM
relic density and direct search experiments. We find that there are ample
parameter space which can interpret the DAMPE data while passing the
constraints. Our explanations, on the other hand, usually imply the existence
of other new physics at the energy scale ranging from $10^7 {\rm GeV}$ to
$10^{11} {\rm GeV}$. Collider tests of our explanations are also discussed.
