An integrated optical apodized sub-wavelength grating waveguide is designed and demonstrated exhibiting high-extinction edge-filter characteristics with a linear roll-off in the dB scale. For a given waveguide cross-sectional geometry with fixed grating duty cycle and period, it has been shown that the apodized device length L-{g} and width W-{m} are the two important parameters deciding the band-edge position, roll-off and broadband extinction around the Bragg wavelength. The experimental results from fabricated devices ( L-{g} = 70\,\,\mu \text{m} and W-{m} = 2.5\,\,\mu \text{m} ) in silicon-on-insulator substrates (device layer 220 nm and buried oxide layer \sim ~2~\mu \text{m} ) show a smooth band-edge roll-off of > 3.5 dB/nm ( \lambda -{edge} \sim ~1550 nm) with a stopband ( \Delta \lambda -{sb}>50 nm) extinction of > 40 dB and a nearly flat-top passband ( \Delta \lambda -{pb}>100 nm) with negligible insertion loss of 0.5 dB. © 1989-2012 IEEE.