We propose an ultrashort and broadband silicon mode-conversion polarization splitter-rotator (PSR) consisting of a taper and a Y-junction both designed by the fast quasiadiabatic dynamics (FAQUAD). The FAQUAD is used to homogeneously distribute adiabaticity over the length of the PSR, providing shortcut to adiabaticity at a shorter device length. The total length of the silicon PSR is 39.2 μm. For a wavelength range from 1.5 μm to 1.6 μm, the PSR exhibits a good performance with > 88% transmission and > 11.4 dB extinction ratio (ER). Simulations also show that the designed devices have good fabrication tolerance.