Quadruple-ridge Flared Horns (QRFHs) have been showing qualified performance as the feed antennas for the reflecting systems in the Square Kilometre Array (SKA). However, due to the offset optics of the SKA reflecting system, identicalilluminations from dual polarizations of the feed would but result in different system performance. This difference would become more severe towards high frequencies and may cause the worse polarization unqualified for the desired specification. In this paper, an asymmetrical QRFH feed working over BandB (4.6–24 GHz) is proposed and optimized to tackle this problem.The asymmetrical Band-B feed is composed of two different and orthogonal pairs of both ridges and sidewall quad-pieces, so as to provide orthogonal polarizations but different illuminations. Simulated results show that, by this asymmetrical design different beamwidths and different combinations of sub-efficiencies can beprovided for two polarizations, so as to eliminate the polarization discrepancy over most of the bandwidth. Benefitting from this elimination, both polarizations of the Band-B feed have now achieved the SKA specification in terms of aperture efficiency
