Based on density functional theory, we study the electronic structures and magnetism of 3d transition metal (TM)-doped two-dimensional (2D) InSe monolayer by means of first-principles methods. The results show that all the doping cases can be easily realized under Se-rich experimental environments. For the Sc- and Cu-doped InSe monolayers, the nonmagnetic semiconducting properties can be retained. The Ti-, Cr- and Ni-doped InSe monolayers possess the half-metal behavior. Moreover, the diluted magnetic semiconductor characteristics can be found in the V-, Mn-, Co-, Fe- and Zn-doped cases. Interestingly, the Ti-, V-, Cr- and Fe-doped 2D InSe systems exhibit ferromagnetic ground states, while antiferromagnetic ground states occur in the Mn-, Co- and Ni-doped InSe monolayers.