We report the observation of a velocity overshoot phenomenon for electrons as well as holes in a GaAs-based p-i-n nanostructure by using transient picosecond Raman spectroscopy. Under the picosecond laser excitation, we have found that the extent of velocity overshoot for electrons is comparable to that of holes. These experimental results have been explained in terms of various carrier scattering processes. Comparisons with results obtained from other III-V semiconductors are also made and a comprehensive discussion is given.