Efficiency of Cerenkov-radiation-type second harmonic generation with absorption loss for second harmonic wave is analytically estimated. Output power reduction for attenuation coefficient of 2.0104 cm1 is calculated 37% (63% output of lossless case). Blue SHG at 443.5 nm is observed by a poled polymer pNAn-PVA waveguide. The wavelength is shorter than the cut-off wavelength of 480 nm.