Compressing picosecond laser pulses to the femtosecond level is an attractive shortcut for obtaining femtosecond laser pulses. However, dechirped pulses generated by nonlinear compression with self-phase modulation (SPM) show obvious pedestals, which are induced by nonlinear chirp accumulation in spectral broadening process and cannot be easily suppressed. Here, we report systematic numerical simulations and experimental studies on self-similar amplification of picosecond pulses in a short gain fiber for obtaining ~100-fs laser pulses with nearly transform-limited (TL) temporal quality. It is demonstrated that self-similar amplification with picosecond seed pulses is only sensitive to pulse duration and pulse energy. Based on this optimization guideline, we built a compact self-similar amplification fiber system with a picosecond fiber laser as the seed source. This system outputs 66-fs pulses with 6.1-W average power at a repetition rate of 30 MHz. Due to the linear chirp produced in self-similar evolution process, compressed pulses show nearly TL temporal quality. It promises an efficient way of obtaining high-quality femtosecond laser pulses from a picosecond laser source.