  By considering the effect of shear viscosity we have investigated the
evolution of a chemically equilibrating quark-gluon plasma at finite baryon
density. Based on the evolution of the system we have performed a complete
calculation for the dilepton production from the following processes:
$q\bar{q}{\to}l\bar{l}$, $q\bar{q}{\to}gl\bar{l}$, Compton-like scattering
($qg{\to}ql\bar{l}$, $\bar{q}g{\to}{\bar{q}}l\bar{l}$), gluon fusion
$g\bar{g}{\to}c\bar{c}$, annihilation $q\bar{q}{\to}c\bar{c}$ as well as the
multiple scattering of quarks. We have found that quark-antiquark annihilation,
Compton-like scatterring, gluon fusion, and multiple scattering of quarks give
important contributions. Moreover, we have also found that the dilepton yield
is an increasing function of the initial quark chemical potential, and the
increase of the quark phase lifetime because of the viscosity also obviously
raises the dilepton yield.
