By employing the technique of asynchronous mode locking, we have successfully demonstrated direct generation of stable 10 GHz 816 fs pulse trains with a supermode-suppression ratio >70 dB from a hybrid mode-locked Er-fiber laser. When the modulation frequency deviates from the cavity harmonic frequency by 15-40 kHz, stable femtosecond soliton pulses are formed. Our results demonstrate that asynchronous mode locking can act as an effective mechanism for achieving a shorter pulse width and for stabilizing high-repetition-rate pulse trains in soliton fiber lasers.