It is commonly believed that the Aharonov-Bohm (AB) effect is a typical feature of the motion of a charged particle interacting with the electromagnetic vector potential. Here we present a magnetophotoluminescence study of type-II InP/GaAs self-assembled quantum dots, unambiguously revealing the Aharonov-Bohm-type oscillations for neutral excitons when the hole ground state changes its angular momentum from lh = 0 to lh = 1, 2, and 3. The hole ring parameters derived from a simple model are in excellent agreement with the structural parameters for this system.