We report on high-average-power operation of a pulsed Raman fiber amplifier at ~1686 nm which cannot be covered by rare-earth-doped fiber lasers. The Raman fiber amplifier was pumped by a home-made 1565.2 nm Q-switched Er,Yb fiber laser and worked at a repetition frequency of 184 kHz. With 0.8 km Raman fiber, 4.4 W of average output power at the 1st order Stokes wavelength of 1686.5 nm was obtained for launched pump power of 16.2 W, corresponding to an optical-to-optical conversion efficiency of 27.2%. Further increasing the pump power, high-order Stokes waves grew gradually, resulting in a total output power of 6.7 W at the 19.2 W launched pump power.