We demonstrate wide-band ultrafast optical pulse generation at 1, 1.5, and 2 μm using a single-polymer composite saturable absorber based on double-wall carbon nanotubes (DWNTs). The freestanding optical quality polymer composite is prepared from nanotubes dispersed in water with poly(vinyl alcohol) as the host matrix. The composite is then integrated into ytterbium-, erbium-, and thulium-doped fiber laser cavities. Using this single DWNT-polymer composite, we achieve 4.85 ps, 532 fs, and 1.6 ps mode-locked pulses at 1066, 1559, and 1883 nm, respectively, highlighting the potential of DWNTs for wide-band ultrafast photonics.