An important ingredient for studying non-equilibrium evolution of partons at RHIC and LHC is to have physical initial conditions for the partonic system. In this paper we investigate the initial conditions with chemical non-equilibrium at RHIC. Considering the parton production, we studied evolution of the partonic medium with chemical non-equilibrium toward a fully equilibrated partonic system. By using a set of rate equations which describe the chemical equilibration of gluons and quarks, and putting different initial conditions, we obtained ...