A mode-locked erbium-doped fiber ring laser that is easy to set up is proposed and experimentally demonstrated to generate a high-repetition-rate optical pulse train with an ultrashort pulse width. The laser combines a rational harmonic mode-locking technique and charcoal nanoparticles as saturable absorbers. Compared to a solely active mode-locking scheme, the scheme with charcoal nanoparticles can remove the supermodes and narrow the pulse width by a factor of 0.57 at a repetition rate of 20 GHz. Numerical simulation of the laser performance is also provided, which shows good agreement with the experimental results.