  We report on the precision predictions for the $e^+e^-\to ZZ\gamma$ process
including $Z$-boson leptonic decays at the ILC in the standard model (SM). The
calculation includes the full next-to-leading (NLO) electroweak (EW)
corrections and high order initial state radiation (h.o.ISR) contributions. We
find that the NLO EW corrections heavily suppress the LO cross section, and the
h.o.ISR effects are notable near the threshold while become small in high
energy region. We present the LO and the NLO EW+h.o.ISR corrected distributions
of the transverse momenta of final $Z$-boson and photon as well as the $Z$-pair
invariant mass, and investigate the corresponding NLO EW and h.o.ISR relative
corrections. We also study the leptonic decays of the final $Z$-boson pair by
adopting the {\sc MadSpin} method where the spin correlation effect is
involved. We conclude that both the h.o.ISR effects and the NLO EW corrections
are important in exploring the $ZZ\gamma$ production at the ILC.
