  The $J/\psi+Z^0$ associated production at the LHC is an important process in
investigating the color-octet mechanism of non-relativistic QCD in describing
the processes involving heavy quarkonium. We calculate the next-to-leading
order (NLO) QCD corrections to the $J/\psi +Z^0$ associated production at the
LHC within the factorization formalism of nonrelativistic QCD, and provide the
theoretical predictions for the distribution of the $J/\psi$ transverse
momentum. Our results show that the differential cross section at the
leading-order is significantly enhanced by the NLO QCD corrections. We conclude
that the LHC has the potential to verify the color-octet mechanism by measuring
the $J/\psi+Z^0$ production events.
