We describe a continuously tunable reflection filter for the 1.2-1.6-microm wavelength range. The filter is a volume-reflection hologram in dichromated gelatin and exhibits high reflection efficiencies (~95%) with narrow spectral bandwidth (~l% FWHM). These filters have been initially designed for use as position-tuned wavelength demultiplexers or channel-selection switches in multichannel optical-fiber systems. A prototype device has been constructed with an insertion loss between input and output single-mode fibers of <3 dB, with bandwidths Deltalambda((1/2))(FWHM) ~1% over the wavelength band.