We implement finite-difference time-domain (FDTD) method to simulate the optical properties of highly polarized InGaN light emitting diodes (LEDs) coupled with metallic grating structure. The Purcell factor (Fp), light extraction efficiency (LEE), internal quantum efficiency (IQE), external quantum efficiency (EQE), and modulation frequency are calculated for different polarized emissions. Our results show that light polarization has a strong impact on Fp and LEE of LEDs due to their coupling effects with the surface plasmons (SPs) generated by metallic grating. Fp as high as 34 and modulation frequency up to 5.4 GHz are obtained for a simulated LED structure. Furthermore, LEE, IQE and EQE can also be enhanced by tuning the coupling between polarized emission and SPs. These results can serve as guidelines for the design and fabrication of high efficiency and high speed LEDs for the applications of solid-state lighting and visible-light communication.