Single crystals of AB-type carbonate apatite were grown by a CaCO3-Na2CO3 flux method under high pressure of Ar gas. The crystals obtained were hexagonal prismatic elongated along the c-axis with the length of 2mm and the diameter of 0.3mm at a maximum. Chemical formula was Ca8.8Na1.2[(PO4)4.8(CO3)1.2]CO3 and the space group was hexagonal P6 with cell parameters a = 0.9379(2)nm, c = 0.6935(1)nm. The detailed crystal structure determined with a reliability factor Rw = 0.047 indicated that the triangular plane of carbonate ion occupying B-site was slanted off the crystallographic mirror plane and the angle of the carbonate triangle with the mirror plane varied depending on Na-substitution of adjacent Ca sites whilst the A-site carbonate ion was parallel to the c-axis.