In order to find new functions of monolayer MoS2 in nanoelectronics or spin electronic devices, using spin-polarized density functional theory (DFT) calculations with on-site coulomb interaction (U), we investigated substitutional doping of Mo atoms of monolayer zigzag MoS2 nanoribbon (ZZ-MoS2 NR) by transition metals (TM) (where TM = Ti, V, Cr, Mn) at the Mo-edge, S-edge, and the middle of the NRs. The results of this study indicate the NR widened irrespective of the doped TM position and type, and the Mo-edge was found as the easiest substitutional position. For ZZ-MoS2 NR doped by Mn, Cr or V atoms, the preferred magnetic coupling state is the edge atoms of S at the S-edge, exhibiting the same spin polarization with TM (named the FM1 state), attributing the NR with metallic magnetism. For Ti-doped monolayer ZZ-MoS2 NR, in addition to the FM1 state, other preferred magnetic coupling state was observed in which the edge atoms of S at the S-edge exhibit the opposite spin polarization with that of Ti (named the FM2 state). Thus, the NR doped by Ti atom possesses metallic (FM1 state) or half-metallic (FM2 state) magnetism. The total magnetic moments of the ZZ-MoS2 NR doped by TM follows a linear relationship as a function of the TM dopants (Mn, Cr, V, and Ti). Under >4% applied strain, the NR doped by Ti atom only presents the characteristics of half-metallic magnetism as the initial one in the FM2 state, and its total magnetic moment always remained 0 μB, i.e., it was not affected by the width of the NR. This study provides a rational route of tuning the magnetic properties of ZZ-MoS2 NRs for their promising applications in nanoelectronics and spin electronic devices.