We present a method to fabricate graded-index multimode polymer optical fibers doped with carbon nanotubes (CNTs). Such fiber structures provide the means to fully utilize the exceptional optical properties of the CNTs. The core region of the fiber is composed of CNTs and polymethyl methacrylate (PMMA) with the addition of diphenyl sulfide (DPS), which acts as the dispersion stabilizer of CNTs in PMMA as well as the dopant to increase the refractive index of the core. Utilizing 2.5 cm of the fiber as a saturable absorber, passively mode-locked lasing with duration of 3.0 ps and repetition rate of 30.3 MHz was demonstrated.