Spin polarization through a four-quantum-dot system is theoretically studied by considering the effects of Zeeman magnetic field, extrinsic Rashba spin–orbit interaction and external magnetic field. We analyze how the resonance and anti-resonance bands are formed by means of the mathematical formula. By adjusting the external magnetic field, the spin polarization can be converted between −100% and 100%, which suggests a physical scheme of an effective magnetically-controlled spin filter. The combined effect of external magnetic field and extrinsic Rashba spin–orbit interaction leads to spin-polarized oscillations. The introduction of the Zeeman magnetic field makes the system easier to be applied as a spin filter. This study provides theoretical insights into the realization of quantum computing, quantum information transmission and development of nanoscale quantum devices.