Slightly tapered Si1-xGex nanowires (NWs) (x = 0.29-0.84) were synthesized via a vapor-liquid-solid procedure using Au as a catalyst. We measured the optically excited carrier dynamics of Si1-xGex NWs as a function of Ge content using optical pump-THz probe spectroscopy. The measured -ΔT/T0 signals of Si1-xGex NWs were converted into conductivity in the THz region. We developed a fitting formula to apply to indirect semiconductors such as Si1-xGex, which explains the temporal population of photo-excited carriers in the band structure and the relationship between the trapping time and the defect states on an ultrafast time scale. From the fitting results, we extracted intra- and inter-valley transition times and trapping times of electrons and holes of Si1-xGex NWs as a function of Ge content. On the basis of theoretical reports, we suggest a physical model to interpret the trapping times related to the species of interface defect states located at the oxide/NW: substoichiometric oxide states of Si(Ge)0+,1+,2+, but not Si(Ge)3+, could function as defect states capturing photo-excited electrons or holes and could determine the different trapping times of electrons and holes depending on negatively or neutrally charged states.