We characterized the beam profiles and polarization states in low-temperature photoluminescence (PL) from a GaAs/InGaAs/GaAs core-multishell nanowire (NW) under CW and pulsed excitations. In the beam profile observation under pulsed excitation, we observed a doughnut-shaped intensity distribution. The beam was also shown to exhibit an axisymmetric distribution in the polarization. These observations indicate that vector beams are generated from the NW. Observed polarization do not correspond to low-order modes of vector beams, suggesting the presence of complicated polarized states reflecting the cavity modes in NWs.