A novel concept for an ultracompact polarization splitter-rotator is proposed by utilizing a structure combining an adiabatic taper and an asymmetrical directional coupler. The adiabatic taper structure is singlemode at the input end while it becomes multimode at the other end. When light propagates along the adiabatic taper structure, the TM fundamental mode launched at the narrow end is efficiently (close to 100%) converted to the first higher-order TE mode at the wide end because of the mode coupling between them. By using an asymmetrical directional coupler that has two adjacent waveguides with different core widths, the first higher-order TE mode is then coupled to the TE fundamental mode of the adjacent narrow waveguide. On the other hand, the input TE polarization does not change when it goes through the adiabatic taper structure. In the region of the asymmetrical directional coupler, the TE fundamental mode in the wide waveguide is not coupled to the adjacent narrow waveguide because of phase mismatch. In this way, TE- and TM- polarized light are separated while the TM fundamental mode is also converted into the TE fundamental mode. A design example of the proposed polarization splitter-rotator is given by using silicon-on-insulator nanowires and the total length of the device is less than 100μm. Furthermore, only a one-mask process is needed for the fabrication process, which is compatible with the standard fabrication for the regular photonic integrated circuits based on SOI nanowires.