A novel reconstruction method for susceptibility-weighted imaging called Magnitude of Complex Fil-tering is proposed to significantly reduce the background phase effects, especially at the air-tissue interface, and to enhance the desirable local structures of veins. In the proposed reconstruction method, a complex-valued magnetic resonance image is acquired using a flow-compensated high-resolution 3D gradient-echo sequence and the magnitude of the complex-valued image is set to 1 so that the phase information, which contains details of the local susceptibility, is emphasized. Then, the nonlinear filter of the Magnitude of Complex Filtering method is applied to the complex-valued image with a constant magnitude. This filter utilizes the magnitude of the low-pass and high-pass filtered complex data to selectively reduce the background phase effects while enhancing the local structures. The filter output is then processed to generate a susceptibility-weighted image. Compared with the conventional susceptibility-weighted images generated by a homodyne high-pass filter, the susceptibility-weighted images from the proposed Magnitude of Complex Filtering method show significant improvement; the undesirable artifacts at the air-tissue interface regions and the brain boundaries are significantly reduced, while the contrast of the local structures of veins is enhanced. In conclusion, the Magnitude of Complex Filtering method successfully reduced most background phase effects without requiring additional processing or scan time.