For a type-II superconductor, when the applied magnetic field is higher than the lower critical value H c1 , the magnetic flux will penetrate into the superconductor and form quantized vortices, which usually are arranged in an Abrikosov lattice. For the newly discovered iron pnictide superconductors, previous measurements have shown that, in electron-doped BaFe 2 As 2 , the vortices form a highly disordered structure 1-3 . In addition, the density of states (DOS) within the vortex cores 1 do not exhibit the Andreev bound states in conventional superconductors 4 -8 . In this Letter, we report the observation of a triangular vortex lattice and the Andreev bound states in hole-doped BaFe 2 As 2 by using a low temperature scanning tunneling microscope (STM). Detailed study of the vortex cores reveals that the spectrum of the Andreev bound states inside the vortex core exhibits a distinct spatial evolution: at the center of the vortex core, it appears as a single peak at 0.5 mV below the Fermi-energy; away from the core center, it gradually evolves into two sub-peaks and they eventually fade out. The drastic differences between the vortex cores of the electron-doped and hole-doped counterparts are illusive to the pairing mechanism of the iron pnictide superconductors.Magnetic flux quantization is one of the important quantum phenomena in the mixed