We report on a femtosecond nonlinear amplification fiber laser system using a vector-dispersion compressor, which consists of a transmission grating pair and multipass cell based Gires–Tournois interferometer mirrors. The mirror is designed with nearly zero group-delay dispersion and large negative third-order dispersion. As a result, the third-order dispersion of the compressor can be adjusted independently to compensate the nonlinear phase shift of amplified pulses to reduce the pulse pedestal. With this scheme, the system outputs $44\mathrm{fs}$ laser pulses with little wing at $26.6\mathrm{W}$ output average power and $531\mathrm{nJ}$ pulse energy, corresponding to $10.8\mathrm{MW}$ peak power.