A high-power and high-pulse-quality femtosecond all fiber laser amplification system is constructed based on the negative third-order dispersion compensation with fiber chirped pulse amplification technology. In the proposed system, the polarization maintaining large mode field of the double-clad Yb-doped fiber and the negative third-order dispersion fiber and the normal polarization maintaining fiber are utilized as the gain medium and mixed fiber stretcher, respectively. Moreover, a pre-compensation of third-order dispersion is implemented while the widening of the time domain is realized, therefore a high-quality and high-power laser is obtained. In the experiment, we use the hybrid fiber stretcher and a 1200 line·mm -1 grating-pair as the compressor, and make the net third-order dispersion of the system approach zero. Consequently, we obtain a high-quality dechirp pulse with central wavelength of 1035 nm and pulse duration of 217 fs. In addition, average output power of 8.5 W at repetition rate of 111 MHz is achieved.