The polarization dependence of directional couplers (DC) formed by silicon-on-insulator (SOI) slot waveguides was studied, and its applications as highly efficient polarization beam splitters (PBSs) and polarization-independent directional couplers (PIDCs) were investigated. The coupling lengths for the quasi-TE and quasi-TM modes may vary with the waveguide geometry due to structural birefringence; thus numerical simulations of the coupling effects in the directional couplers with different aspect ratios and waveguide spacing were conducted to obtain the optimal design parameters for high efficiency as well as compact device size. The lengths of the coupling regions of the designed PBS and PIDC are 47.61 and 23.13 μm, respectively, and they delivered good performance, with an extinction ratio greater than 20 and 1 dB bandwidth larger than 100 nm. The tolerance of fabrication error in the practical device is also discussed.