The existence of topological hinge states is a key signature for a newly proposed class of topological matter, the second-order topological insulators. In the present paper, a universal mechanism to generate chiral hinge states in the ferromagnetic axion insulator phase is introduced, which leads to an exotic transport phenomenon, the quantum anomalous Hall effect (QAHE) on some particular surfaces determined by both the crystalline symmetry and the magnetization direction. A realistic material system, Sm-doped Bi2Se3, is then proposed to realize such exotic hinge states by combining first-principles calculations and Green’s function techniques. A physically accessible way to manipulate the surface QAHE is also proposed, which makes it very different from the QAHE in ordinary 2D systems.The second-order topological states—chiral hinge states—are predicted in axion insulators, ferromagnetic insulating materials with quantized electromagnetic response. The authors predict such states to occur in Sm-doped Bi2Se3.