An ultra-broadband polarization beam splitter (PBS) with low excess loss (EL) and a high extinction ratio (ER) is proposed and demonstrated for the case with 340 nm thick silicon-on-insulator waveguides. Here the PBS is realized by using cascaded adiabatic dual-core tapers, which consist of a strip core and a subwavelength-grating core. For the designed PBS, which has a 33.6 µm long mode-evolution region, the ELs are ${ \lt }{0.3}\;{\rm dB}$<0.3dB, and the ERs are ${ \gt }{20}\;{\rm dB}$>20dB for both TE and TM polarizations in an ultra-broad bandwidth of ${ \gt }{270}\;{\rm nm}$>270nm (1400-1670 nm) in theory. For the fabricated PBS, the measured bandwidths for achieving ERs of ${\sim}{20}$∼20 and ${\sim}{25}\;{\rm dB}$∼25dB are 240 and 220 nm, while the 1 dB bandwidth is as large as 230 nm, which are the largest bandwidths reported to date, to the best of our knowledge.