We report quasielastic neutron scattering results on an amorphous polyimide (AURUM) in a temperature range from 10 to 300 K below the glass transition temperature T-g(=250 degrees C). As temperature increases from 10 K, anharmonic excess scattering intensity appears at around 200 K or about 300 K below T-g. This excess scattering is very similar to the so-called fast process in picosecond order observed for glass-forming polymers as well as organic and inorganic low molecular weight glass-forming materials. We first analyzed the spectra in a simple way assuming validity of the Bose scaling for the vibrational density of states and a Lorentzian for the additional relaxational process, and found that the excess scattering intensity appears in the frequency range below the Boson peak and the characteristic time is independent of temperature which are common features for the fast processes reported previously. The second analysis using the recent vibration-relaxation (VR) model, which is more realistic, indicated that softening of the vibrational modes may play an important role for the change of spectra from inelastic-like to quasielastic-like. Nevertheless, relaxational process is still necessary to describe the excess scattering although the temperature range examined is very far below T-g.