A compact asymmetrical directional coupler (ADC), which is composed of a strip and a tilted subwavelength gratings (TSWG) waveguide, is proposed to realize a broadband and high-extinction-ratio polarization beam splitter (PBS). In addition to conventional SWG structural parameters, such as its period and duty cycle, a TSWG waveguide provides an extra degree of freedom to solely adjust the TE modal effective index for more accurate phase matching. Hence the TE polarization state is coupled more efficiently in the ADC system, and then the extinction ratio (ER) is consequently improved. The simulation of our proposed device demonstrated a higher coupling efficiency and an ultrahigh ER of 34.2 dB for the TM polarization state at the center wavelength around 1550 nm. The operating bandwidth of the TM polarization state defined as the spectral range, with ER higher than 20 dB, is determined to be as broad as 75 nm. And, with an assisted hybrid plasmonic waveguide at the end of the cross port, the achieved bandwidth of the TE polarization state is as broad as 133 nm. They are much broader than those of other DC/ADC implemented PBS devices. Moreover, further analysis shows that the tilting angle of the TSWG waveguide has much higher fabrication tolerance than changing SWG duty cycle.