We have numerically presented an actively mode-locked fiber laser with tunable repetition rate based on phase modulator. By finely optimizing intra-cavity parameters, the ultrashort pulses with tunable repetitive frequency at giga hertz level can be easily generated due to the balance between dispersion and nonlinearity in the fiber laser cavity. When the pulse frequency is changed from 1.0 GHz to 4.2 GHz, the spectral width increases from ~15.65 nm to ~27.25 nm. In addition, the corresponding pulse duration decreases from ~81.59 ps to ~31.57 ps. Moreover, these output pulses with giga hertz repetitive rates and the picosecond widths can be further compressed by using the reasonable dispersion medium. For the pulse regime with repetition frequency at giga hertz level, the obtained smallest pulse duration is about ~62 fs based on chirp pulse compression. We hope that these simulation results can promote further research and application in the ultrashort pulse lasers with high repetition rate.