Employing the first-principles calculation based on the density functional theory, the geometries, magneto-electronicproperties, and strain effects of the zigzag-edged InSe nanoribbons with the Se-edge saturated by H atoms and In-edge terminated by various non-metallic elements X( X= H, B, N, P, F and Cl) are studied. The calculated formation energy and Forcite annealing simulations show that the H-ZN(7)-X has a stable geometry. For F- and Cl- terminated ribbons, they have a magnetic metallic property similar to that in the case of H termination, and for the N termination the nanoribbon has the strongest magnetic property. However, the B and P terminations cause the magnetic properties at the ribbon edge to completely disappear, particularly when the mechanical strain is applied. The magnetic stability of H-ZN(7)-N is enhanced, and the spin polarization efficiency (SP) at the Fermi level can be effectively modulated in a range from zero to 92%, which means that it is possible to design a mechanical switch for controlling the spin transport at low bias. The strain modulating mechanism is related to the fact that the variation of strain-induced bond length leads the unpaired electrons to be redistributed or disappear. The magnetic properties of N-ZN(7)-N are mainly derived from the porbitals of In, Se and N atoms, thus it is very important to develop non-transition metal magnetic materials.