Fe₃GeTe₂ monolayer is one of the currently fabricated 2-dimensional (2D) ferromagnetic materials. Based on the first principle of density functional theory, we here study the structural stability and magneto-electronic properties of nanoribbons NR(n) obtained by cutting 2D Fe₃GeTe₂. The calculated binding energy and molecular dynamics simulation results identify that nanoribbons are rather stable. The large magnetic moment and magnetized energy prove the extremely high magnetism stability for NR(n). Moreover, with the increase of the width, the magnetic moment of the nanoribbons generally increases, and gradually tends to a stable value. In particular, the nanoribbons possess a high spin polarization efficiency at the Fermi level (SP_F). For example, the SPF for NR(5) is up to 100%. With the width variation of the nanoribbons, the SP_F has a significant odd-even oscillating effect, that is, the spin-polarization of the odd nanoribbons is higher than that of the adjacent even nanoribbons, especially when the width is in the range of n ≤ 12. This means that the α-spin and β-spin are quite different in the density of states at the Fermi level when the width is odd or even. This may be caused by the difference of the quantum confinement effect for the odd or even nanoribbons, respectively. Meanwhile, when the width of the nanoribbons is wide enough, the odd-even oscillation effect of the spin polarizability is stabilized in a relatively small range, and the nanoribbons finally tend to be 2D Fe₃GeTe₂ monolayer. The nanoribbons have an obvious advantage on SP_F over the 2D Fe₃GeTe₂ monolayer. In addition, the calculation of the strain effect demonstrates that the strain can flexibly tune the SP_F varying from approximately zero to 85.6%, and the SP_F reaches a maximum of 85.6% at a stretch of 4%, which is a fairly high value; then reaches a minimum at a stretch of 8%, almost being zero, which means that a mechanical switch can be designed to control the low-bias spin transition, allowing it work between high spin polarization and spin unpolarization.