A mechanism to generate a spin-polarized current in a two-terminal zigzag silicene nanoribbon is predicted. As a weak local exchange field that is parallel to the surface of silicene is applied on one of edges of the silicene nanoribbon, a gap is opened in the corresponding gapless edge states but another pair of gapless edge states with opposite spin are still protected by the time-reversal symmetry. Hence, a spin-polarized current can be induced in the gap opened by the local exchange field in this two-terminal system. What is important is that the spin-polarized current can be obtained even in the absence of Rashba spin-orbit coupling and in the case of the very weak exchange filed. That is to say, the mechanism to generate the spin-polarized currents can be easily realized experimentally.We also find that the spin-polarized current is insensitive to weak disorder.