A millimeter-wave (MMW) windmill-shaped magnetoelectric-dipole antenna with broadband circular polarization and wide axial-ratio (AR) beamwidth is presented. Good circular polarization performances of the proposed antenna are contributed to excellent performances of the magnetoelectric-dipole, the benefit of windmill shape and the sequential feed scheme by a circular microstrip line. Simulation results show that the antenna obtains a wide impedance bandwidth of 58.8% over the band 30~55 GHz, a stable 3-dB AR bandwidth of 30% across the band 34~46 GHz. And the gain is higher than 6 dBic within the AR bandwidth, with the highest gain of 9.2 dBic at 45 GHz. In addition, a unidirectional and stable pattern has also been achieved.