  The model-independent reconstruction of the energy spectra of
$\overline{\nu}^{}_e$, $\nu^{}_e$ and $\nu^{}_x$ (i.e., $\nu^{}_\mu$,
$\nu^{}_\tau$ and their antiparticles) from the future observation of a
galactic core-collapse supernova (SN) is of crucial importance to understand
the microscopic physics of SN explosions. To this end, we propose a practically
useful method to combine the multi-channel detection of SN neutrinos in a large
liquid-scintillator detector (e.g., JUNO), namely, the inverse beta decay
$\overline{\nu}^{}_e + p \to e^+ + n$, the elastic neutrino-proton scattering
$\nu + p \to \nu + p$ and the elastic neutrino-electron scattering $\nu + e^-
\to \nu + e^-$, and reconstruct the energy spectra of $\overline{\nu}^{}_e$,
$\nu^{}_e$ and $\nu^{}_x$ by making the best use of the observational data in
those three channels. In addition, the neutrino energy spectra from the
numerical simulations of the delayed neutrino-driven SN explosions are
implemented to demonstrate the robustness of our method. Taking the ordinary
matter effects into account, we also show how to extract the initial neutrino
energy spectra in the presence of neutrino flavor conversions.
