We study the abnormal quantum transport through quantum point contact systems with Rashba effect and lateral spin-orbit coupling under asymmetric confinement geometries. We find that for a certain range of Rashba interaction strength, the conductance has a weak plateau around 0.8×2e^2/h. The value of this anomalous plateau is dependent on the voltage bias of the asymmetric confinement. We find that for a certain range of voltage bias, this weak plateau is lowered slightly with increasing the voltage bias. Furthermore, we find that the asymmetric confinement gives rises to a nonzero spin polarization due to the Rashba spin-orbit coupling. Therefore, we can make such quantum point contact spin-polarizer by purely electrical means in the absence of any applied external magnetic field.