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AMoRE-II is the second phase of the Advanced Molybdenum-based Rare process Experiment aiming to search for the neutrino-less double beta decay of 100Mo isotopes using ~ 200 kg of molybdenum-containing cryogenic detectors. The AMoRE-II needs to keep the background level below 10-5 counts/keV/kg/year with various methods to maximize the sensitivity. One of the methods is to have the experiment be carried out deep underground free from the cosmic ray backgrounds. The AMoRE-II will run at Yemilab with ~ 1,000 m depth. However, even in such a deep underground environment, there are still survived cosmic muons, which can affect the measurement and should be excluded as much as possible. A muon veto detector is necessary to reject muon-induced particles coming to the inner detector where the molybdate cryogenic detectors are located. We have studied the possibility of using an extruded plastic scintillator and wavelength shifting fiber together with SiPM as a muon veto system. We found that the best configuration is two layers of plastic scintillators (PSs, 150 cm x 25 cm x 1.2 cm) with two WLS fibers per groove, which could separate radiogenic gammas well with muon detection efficiency above 99.4% along the length of the PS. Based on the expected flux from a prototype measurement at a 700 m deep underground, we found that the dead time of the muon veto system for AMoRE-II at the Yemilab with a 1 ms veto window is 0.6% of whole muon events.