Single-layer ultra-narrow MoS2 armchair nano-ribbons (AMoS2NRs) are studied by density functional theory (DFT) in this paper. The width of AMoS2NRs is classified by the number of dimer lines (N) across the ribbons. Ultra-narrow bare AMoS2NRs with N=4, 5, 6 and 7 are indirect band gap semiconductors, different from cases where AMoS2NRs with N>7 and N=3. The reason is ascribed to the different ratio of states provided by d-orbitals of Mo atoms to states by p-orbitals of S atoms for AMoS2NRs with different widths. After passivation of edge atoms by hydrogen, most AMoS2NRs become direct band gap semiconductors except for AMoS2NR with N=4.