We show that the critical current of the Josephson junction consisting of superconducting electrodes coupled through a nanowire with two conductive channels can reveal the multiperiodic magnetic oscillations. The multiperiodicity originates from the quantum mechanical interference between the channels affected by both the strong spin-orbit coupling and the Zeeman interaction. This minimal two-channel model is shown to explain the complicated interference phenomena observed recently in Josephson transport through Bi nanowires.