Based on density functional theory, the electronic structure and magnetic properties of monolayer PtSe2 doped with different atoms were studied. The Pt and Se atoms are replaced by a transition metal atom (Mn) and a non-metal atom X (X = N, P, As), respectively. The pristine monolayer PtSe2 is a semiconductor with an indirect band gap of 1.352 eV. For one non-metal atom doping, the doped system exhibits indirect band gap magnetic semiconducting properties and the magnetic moment is less than 1 μB and mainly comes from the hybridization of Pt-5d and X-p orbitals. The N-Doped system still retains the magnetic semiconducting properties under strain (from -10% to 13%) and the band gap varies from 0.059 eV to 1.308 eV. For two X doped systems, three different configurations are considered. The doped systems retain the indirect band gap semiconducting properties except for the third nearest neighbor N-doped system (direct band gap). But, for all N-doped and the second nearest neighbor P-doped systems, the magnetic moment increases to more than double. Meanwhile, all X-doped monolayer PtSe2 systems exhibit p-type semiconducting characteristics. For (Mn, X) co-doped systems, the magnetic moments are mainly localized in the Mn 3d orbital and there is strong p-d hybridization between Mn atoms and X atoms. The (Mn, N/P) co-doped system still exhibits magnetic semiconducting properties. These results are important for designing semiconductor devices and electronic spin devices based on monolayer PtSe2.