We investigate the enhancement of spin polarization in a quantum wire in the presence of a constriction and a spin-orbit coupling segment. It is shown that the spin-filtering effect is significantly heightened in comparison with the configuration without the constriction. It is understood in the studies that the constriction structure plays a critical role in enhancing the spin filtering by means of confining the incident electrons to occupy one channel only while the outgoing electrons occupy two channels. The enhancement of spin filtering has also been analyzed within the perturbation theory. Because the spin polarization arises mainly from the scattering between the constriction and the segment with spin-orbit coupling, the subband mixing induced by spin-orbit interaction in the scattering process and the inferences result in higher spin-filtering effect.