Utilizing first-principles calculations, the electronic structures, magnetic properties and band alignments of monolayer MoS2 doped by 3d transition metal atoms have been investigated. It is found that in V, Cr, Mn, Fe-doped monolayers, the nearest neighboring S atoms (SNN) are antiferromagnetically polarized with the doped atoms. While in Co, Ni, Cu, Zn-doped systems, the SNN are ferromagnetically coupled with the doped atoms. Moreover, the nearest neighboring Mo atoms also demonstrate spin polarization. Compared with pristine monolayer MoS2, little change is found for the band edges' positions in the doped systems. The Fermi level is located in the spin-polarized impurity bands, implying a half-metallic state. These results provide fundamental insights for doped monolayer MoS2 applying in spintronic, optoelectronic and electronic devices.