The structural and electronic properties of mono-vacancy (MV) defect in graphene-based Mobius strip (GMS) are studied in the framework of density functional theory (DFT) combined with the molecular dynamics (MD) simulations. Two kinds of MV defects are observed: the 59-type MV (a configuration with one pentagon and one nonagon ring) located at the curved areas of Mobius strip, and the 5566-type MV (a configuration with two pentagon and two hexagon rings) with one sp(3) hybridized carbon appeared in the twisted areas. The 5566-type MV defect is the most stable configuration at 0 K, while the DFT-MD calculations show that it is unstable at room-temperature and will transform into a 59-type MV. Additionally, the melting behavior of GMSs is investigated through empirical potential MD simulations, and we find that their melting temperatures are about 2750 K, which is lower than that of carbon nanotubes and graphene.