A compact polarization splitter-rotator based on a silicon-on-insulator rib asymmetrical directional coupler with SiO2 top-cladding is proposed. Unlike previously reported PSRs which specifically required the top-cladding material to be different from the bottom cladding in order to break the symmetry of the waveguide cross-section, our proposed PSR has no such limitation on the top-cladding due to the horizontal asymmetry of the rib waveguide. In addition, the device is highly compact and has a total length as short as 24 μm. Numerical simulation shows that a high conversion efficiency of ~97% is obtained at the wavelength of 1550 nm. With the width variation of ± 15 nm and the gap variation of ± 50 nm, the PSR still has high ER of 12 dB at the cross-port, showing large fabrication tolerance. This device can be cascaded to improve the performance at the through port and an example of a two-stage PSR is presented. The mode conversion between the strip waveguide and the rib waveguide is also discussed.