We report on a crystal phase-dependent photoluminescence (PL) polarization effect in individual wurtzite GaAs nanowires with a zinc blende GaAsSb insert grown by Au-assisted molecular beam epitaxy. The PL emission from the zinc blende GaAsSb insert is strongly polarized along the nanowire axis while the emission from the wurtzite GaAs nanowire is perpendicularly polarized. The results indicate that the crystal phases, through optical selection rules, are playing an important role in the alignment of the PL polarization in nanowires besides the linear polarization induced by the dielectric mismatch. The strong excitation power dependence and long recombination lifetimes (∼4 ns) from the wurtzite GaAs and zinc blende GaAsSb-related PL emission strongly indicate the existence of type II band alignments in the nanowire due to the presence of nanometer thin zinc blende segments and stacking faults in the wurtzite GaAs barrier.