Femtosecond optical frequency combs have introduced revolutionary promotions to precision optical spectroscopy and metrology, and have been hot topics of laser technologies and applications for two decades. In this article, the affects of intracavity dispersion and mode-locking mechanism on carrier-envelope phase slip frequency(fCEO) of femtosecond laser pulse trains were researched based on a femtosecond Ytterbium-doped fiber laser with 250 MHz repetition rate. By optimizing the intracavity dispersion, pumping power, and detection methods, 49 dB signal-noise-ratio fCEO beat signal was obtained which then was stabilized it to a stability of 3.2×10-10 in 1 second, and a stability of 3.4×10-13(1 s) of frep was also achieved. In addition, the effects of pulse chirping on the output pulse duration of a fiber amplifier was researched based on a piece of large-mode-area photonic crystal Yb doped fiber. Under 60 W of pumping power from a laser diode at 976 nm wavelength, 23 W average output power from the amplifier with 66 fs pulse duration and 250 MHz repetition rate was achieved when the seed pulses were carring -3.8×104 fs2 pre-chirping dispersion.