  The $Q^2$ evolution of fragmentation function in non-equilibrium QCD by using
DGLAP evolution equation may be necessary to study hadron formation from
quark-gluon plasma at RHIC and LHC. In this paper we study splitting functions
in non-equilibrium QCD by using Schwinger-Keldysh closed-time path integral
formalism. For quarks and gluons with arbitrary non-equilibrium distribution
functions $f_q({\vec p})$ and $f_g({\vec p})$, we derive expressions for quark
and gluon splitting functions in non-equilibrium QCD at leading order in
$\alpha_s$. We make a comparison of these splitting functions with that
obtained by Altarelli and Parisi in vacuum.
