In this paper we have investigated the dynamics of photo-generated charge carriers in a series of aerotaxy-grown GaAs nanowires (NWs) with different levels of Zn doping. Time-resolved photo-induced luminescence and transient absorption have been employed to investigate radiative (band edge transition) and non-radiative charge recombination processes, respectively. We find that the photo-luminescence (PL) lifetime of intrinsic GaAs NWs is significantly increased after growing an AlGaAs shell over them, indicating that an AlGaAs shell can effectively passivate the surface of aerotaxy-grown GaAs NWs. We observe that PL decay time as well as PL intensity decrease with increasing Zn doping, which can be attributed to thermally activated electron trapping with the trap density increased due to the Zn doping level.