  $J/\psi$ suppression/production is one of the main signature of quark-gluon
plasma detection at RHIC and LHC. In order to study $j/\psi$
suppression/production in high energy heavy-ion collisions at RHIC and LHC, one
needs to prove the factorization theorem of $j/\psi$ production in
non-equilibrium QCD medium, otherwise one will predict infinite cross section
of $j/\psi$. In this paper we prove factorization theorem of $j/\psi$
production in non-equilibrium QCD at RHIC and LHC at all order in coupling
constant.
