We report a ring-cavity thulium fiber laser mode locked with a single-wall carbon nanotube absorber used in transmission. A carboxymethyl cellulose polymer film with incorporated carbon nanotubes synthesized by the arc discharge method has an absorption coinciding with in the amplification bandwidth of a Tm-doped fiber. This laser is pumped by an erbium fiber laser at 1.57 microm wavelength and produces a 37 MHz train of mode-locked 1.32 ps pulses at 1.93 microm wavelength with an average output power of 3.4 mW.