We investigate the period halving of persistent currents (PCs) of non-interacting electrons in isolated mesoscopicMobius ladders without disorder, pierced by Aharonov-Bohm flux. The mechanisms of the period halving effectdepend on the parity of the number of electrons as well as on the interchain hopping. Although the data of PCsin mesoscopic systems are sample specific, some simple rules are found in the canonical ensemble average, forexample, all the odd harmonics of the PCs disappear and the signals of even harmonics are non-negative.