Spin-dependent electron transmission through a helical membrane, taking account of linear spin-orbit interaction, has been investigated by numerically solving the Schrödinger equation in cylindrical coordinates. It is shown that the spin precession is affected by the magnitude of geometric parameters and chirality of the membrane. This effect is also explained analytically using perturbation theory in the weak coupling regime. In the strong coupling regime, the current spin polarization is evident when the number of the open modes in leads is larger than that of the open channels in the membrane. Moreover, we find that the chirality of the helical membrane can determine the orientation of current spin polarization. Therefore, one may get totally opposite spin currents from helical membranes rolled in different directions.