Graphene is attracting attention in electrical and optical research fields recently. We measured the optical absorption characteristics and polarization dependence of single-layer graphene (SLG) on sub-micrometer Si waveguide. The results for graphene lengths ranging from 2.5 to 200 $mu$ m reveal that the optical absorption by graphene is 0.09 dB/$mu$ m with the TE mode and 0.05 dB/$mu$ m with the TM mode. The absorption in the TE mode is 1.8 times higher than that in the TM mode. An optical spectrum, theoretical analysis and Raman spectrum indicate that surface-plasmon polaritons in graphene support TM mode light propagation.