In this paper the single mode condition of silicon-on-insulator (SOI) rib waveguide with large cross section is investigated based on the effective index method (EIM) by using numerical computation and analytical derivation with the consideration of the polarization effects. A polarized single-mode condition for SOI rib waveguide with large cross section is presented, the results from analytical derivation are highly concordant with that from numerical computation. For the vertical single-mode condition, the deviations between HE and EH modes correlate oppositely with the total rib height of rib waveguide, and the critical rib height ratio gradually approaches but never equals to 0.5 with the increase of the total rib height. There, HE mode and EH mode are commonly known as quasi-transverse-electric (TE) mode and quasi-transverse-magnetic (TM) mode respectively. The deviation of the critical rib width between HE and EH modes for the lateral single-mode condition is relatively small, which is a function of the rib height ratio but irrelevant to the total rib height for the specified index profile. The fact that the total rib height, index profile, and polarization of modes have effects on the single-mode condition of SOI rib waveguide with large cross section was demonstrated in this work, which was not discussed in the previous works. The results in this work can give guidance to design, simulation and fabrication of SOI rib waveguide with large cross section in practical applications.