We have studied magnetic structure and properties of Ga-substituted Pb-hexaferrites having the stoichiometry of PbFe12-xGaxO19 with x=6 (i.e., Fe:Ga=1:1). According to the neutron diffraction results, this compound is characterized by a collinear spin structure below its Curie temperature (∼325 K). Analysis of the neutron diffraction patterns further indicates that the magnetic-moment direction of Fe3+ ions located at the octahedral 2a sublattice is downward while that of the unsubstituted PbFe12O19 is upward at room temperature. With decreasing temperature, the Fe3+ magnetic moment at the octahedral 2a sublattice undergoes a reorientation to the upward direction while that of the unsubstituted PbFe12O19 remains upward down to 5 K. This selective local spin reversal at the 2a sublattice of PbFe6Ga6O19 was attributed to the weakening of the superexchange interaction between the octahedral 2a site and the tetrahedral 4fIV site upon the preferential substitution of Ga ions for Fe ions at these two neighboring sites. Comparison of the neutron diffraction results with dc magnetization responses and ac susceptibilities further indicates that the paramagnetic-ferrimagnetic transition at ∼325 K (Tc) is followed by the local spin reversal at lower temperatures.