Diffractive periodic-structure-based grating couplers (GCs) are the most widely used devices for light coupling between optical fibers and integrated photonic devices. However, conventional GCs have limited wavelength operation and are polarization specific, which is due to the intrinsic radiation angle dependency on both wavelength and polarization. Here we propose and experimentally demonstrate a polarization-splitting dual-band grating coupler (PS-DBGC) for polarization diversity and wavelength division (de)multiplexing (WDM) operation. The four-port two-dimensional PS-DBGC is based on a periodically arranged structure with square holes, and requires only a single etch step in a 340-nm silicon-on-insulator platform. The simulation predicts that the maximum coupling efficiency (CE) of the proposed PS-DBGC is -2.8 dB and -4.6 dB for the O- and C-band, respectively. The measured peak CEs of the fabricated device are -4.7 dB at 1280 nm and -8.4 dB at 1522 nm. We anticipate that this PS-DBGC could potentially improve the performance of any future integrated WDM passive optical network.