The rectification behaviours in organic magnetic/nonmagnetic co-oligomer spin rectifiers are investigated theoretically. It is found that both the charge current and the spin current through the device are rectified at the same time. By adjusting the proportion between the magnetic and nonmagnetic components, the threshold voltage and the rectification ratio of the rectifier are modulated. A large rectification ratio is obtained when the two components are equal in length. The intrinsic mechanism is analysed in terms of the asymmetric localization of molecular orbitals under biases. The effect of molecular length on the rectification is also discussed. These results will be helpful in the future design of organic spin diodes.