We use magnetization measurements, high-resolution angle-resolved photoemission spectroscopy (ARPES), and density functional theory (DFT) calculations to study the electronic properties of Au2Pb, a topological superconductor candidate. The magnetization measurements reveal three discontinuities at 40, 51, and 99 K that agree well with reported structural phase transitions. To measure the band structure along desired crystal orientations, we utilized polishing, sputtering, and annealing to obtain clean flat sample surfaces. ARPES measurements of the Au2Pb (111) surface at 110 K shows a shallow hole pocket at the center and flower-petal-like surface states at the corners of the Brillouin zone. These observations match the results of DFT calculations relatively well. The flower-petal-like surface states appear to originate from a Dirac-like dispersion close to the zone corner. For the Au2Pb(001) surface at 150 K, ARPES reveals at least one electron pocket between the Γ and M points, consistent with the DFT calculations. Our results provide evidence for the possible existence of a Dirac state in this material.