An all-fiber actively mode-locked thulium-doped fiber laser (AML-TDFL) based on a 10 GHz bandwidth electro-optic intensity modulator (EOM) providing flexible picosecond pulses at 1980 nm is presented. The EOM is driven by electrical pulses rather than traditional sine-wave signals. The repetition rate of output pulses was 21.4 MHz at fundamental mode-locking, which could be scaled up to 1.498 GHz through the 70th order harmonic mode-locking, and the shortest measured output pulse width was 38 ps. Furthermore, the output pulse width could be tuned by either adjusting the modulation frequency with small detuning or changing the width of these driving electrical pulses without frequency detuning. In our work, the stability of these mode-locked pulses obtained from the AML-TDFL was superior; for instance, the measured supermode suppression ratio of 1.498 GHz pulses train was up to 48 dB.