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: $qbar{q}{to}lbar{l}$, $qbar{q}{to}glbar{l}$, Compton-like scattering ($qg{to}qlbar{l}$, $bar{q}g{to}{bar{q}}lbar{l}$), gluon fusion $gbar{g}{to}cbar{c}$, annihilation $qbar{q}{to}cbar{c}$ 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.
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