We propose a theoretical design of a high-speed wavelength-selective variable optical attenuator (VOA) constructed by a waveguide-type Raman amplifier and two directional couplers. The VOA can attenuate each incident WDM wavelength individually and simultaneously in a few tens of picoseconds by applying the corresponding pumping wavelength to the Raman amplifier. We define two operation modes, which may allow the attenuation ratio to decrease or increase by increasing the amplification rate of the Raman amplifier. The profile of the attenuation curves of the two operation modes can be flexibly determined by properly selecting the phase angles of the directional couplers. The guidelines to determine these phase angles of the two directional couplers are provided after the operational analyses.