The electronic structure, magnetic properties and stability of transition-metal (TM) doped armchair MoS2 nanoribbons (AMoS2NRs) with full hydrogen passivation have been investigated using density functional theory. The hydrogen passivated AMoS2NRs are non-magnetic semiconductors, but TM doping can make the AMoS2NRs display diverse characteristics (such as non-magnetic metal, magnetic semiconductor, non-magnetic semiconductor and semi-metal properties), in which a transition of the electronic and magnetic properties is observed. Electronic structure analysis shows that the magnetism of the TM-doped AMoS2NRs is concentrated on the TM dopant and the edge Mo atoms, which mainly comes from the competition between the exchange splitting and crystal-field splitting. More importantly, Mn-doped AMoS2NRs may be good candidates for spintronic devices due to their good ferromagnetism with long-range FM magnetic coupling, reliable Curie temperature and high stability. These interesting findings on AMoS2NRs may open the possibility of their application in nanodevices and spintronic devices based on low-dimensional nanostructures.