Dileptons have large mean free paths due to their small cross sections for electromagnetic interaction in plasma. Therefore they are considered to be an important probe for the formation and evolution of the quark matter. In this work, we calculate the dilepton production of quark-gluon plasma (QGP) produced in Au197+ Au197 central collisions at relativistic heavy ion collider (RHIC) energy based on the evolution model of a chemically equilibrating viscous QGP. The evolution of the QGP system is described by a set of coupled relaxation equations containing the master equations of partons, the equation of baryon number conservation and equation of energy-momentum conservation. Solving the set of evolution equations, one can obtain the evolution of temperature T, quark chemical potential q, fugacities q for quarks and g for gluons. To discuss the shear viscosity of QGP, the contributions of the elastic scattering of quarks qqqqand gluons gggg, as well as the inelastic scattering process of gluons ggggg are included. Based on the evolution model including the viscosity, we perform a complete calculation of the dilepton production, including the processes of quark-antiquark annihilation qqll, next-order annihilation qqgll, Compton-like scattering qg qll, qg qll, multiple scattering of quarks, as well as gluon fusion gg cc, annihilation qqcc. It is found that the spectra from the quark-antiquark annihilations qqll and qqgll are dominated. The contributions from multiple scattering cannot be neglected. We also find that the dilepton yields remarkably decrease with considering an additional gluon inelastic process in the calculation compared with the results with considering only elastic scatterings of quarks and gluons. This indicates that the evolution of QGP system is accelerated and the evolution time is shortened by the inelastic scatterings of gluons.
