Abstract: The magnetic flux dependence of energy and supercurrent in mesoscopic d-wave symmetric and asymmetric superconducting loops is investigated by numerically solving the Bogoliubov-de Gennes equations self-consistently. For square loops, we find an hc/e-flux periodicity in energy and supercurrent and demonstrate that the flux periodicity is sensitive to the hole size and the superconducting pairing strength as well as temperature. The hc/2e-periodic behavior can be restored almost entirely when we displace the central hole sufficiently out of the center of the sample. In rectangular loops, the discrete current-carrying low-energy spectrum can exist for an odd winding number of the order parameter.