Several half-metallic graphene-like nanosheets, namely halogen atom adsorbed InSe-X (X = F, Cl, Br and I) nanosheets, are predicted by first-principles calculations. Then, their structural, electric and magnetic properties are studied in detail. The calculated negative adsorption energies of these InSe-X nanosheets ensure that they attain stable adsorption structures, which suggests that they may be prepared experimentally. The pristine InSe monolayer is a typical semi-conductor, whereas it is interesting that the X ion (X = F, Cl, Br and I) adsorbed InSe-X nanosheets are electronically conductive. They can be promising and good candidates for applications of half-metallic 2D materials. The calculated magnetic moments of these nanosheets are close to 1.0 µ B. In the InSe-F nanosheet, there are sp2 hybridized orbitals due to the crystal field effect, and its electroconductibility, half-metallicity and magnetic moments originate from the In and Se ions, not the F ion. However, in InSe-X (X = Cl, Br and I) nanosheets, there are sp3 hybridized orbitals, and their electroconductibility, half-metallicity and magnetic moments originate mainly from X ions, together partially with the In and Se ions.