Carbon-based nanomaterials have become a long-term research hotspot in the fields of material science and nanotechnology. Carbon nanotubes as one-dimensional nanomaterials have shown great application value in the fields of electronics and optoelectronics. Herein, stable mode-locked pulsed lasers in both 1.5- and 2-μm bands were achieved by combining and balancing the stimulated emission effect of rare-earth ions and saturable absorption effect of carbon nanotubes. In the Er-doped fiber laser, pulses with a SNR of 61 dB and a peak power of 2.97 W were achieved at the wavelength of 1565.8 nm. Meanwhile, bound states were observed in the same laser, where the time delay of pulses was adjustable from 9.84 to 21.77 ps by tuning the pump power and polarization state. In the Tm-doped laser, output pulses were obtained at the wavelength of 1921.0 nm with a 60-dB SNR and a 12.82-W peak power. These results demonstrate that carbon nanotubes are ideal candidates for saturable absorber in mode-locked fiber lasers, which can be applied to a variety of applications, including fiber optic sensing, optical communication, and nanoscale processing.