We investigate the exciton Mott transition (EMT) by using optical pump-terahertz probe spectroscopy on GaAs, with realizing the condition of Mott's gedanken experiment by the resonant excitation of 1s excitons. We show that an anomalous metallic phase emerges on the verge of the EMT as manifested by a peculiar enhancement of the quasiparticle mass and scattering rate. From the temperature and density dependence, the observed anomaly is shown to originate from the electron-hole (e-h) correlation which becomes prominent at low temperatures, possibly suggesting a precursor of e-h Cooper pairing.