Considered the Drell-Yan background in the intermediate invariant mass region, the dilepton production in an expanding hot baryon-rich quark-gluon matter fire-cylinder has been studied based on a previously established relativistic hydrodynamic model. It is found that with increasing the rapidity the dilepton yield is strongly suppressed. Such a characteristic, signaling the formation of the baryon-rich quark-gluon matter, can be tested in future experiments at Brookhaven and CERN.