Femtosecond laser has important applications in such fields as industrial processing, laser sensing, military defense, and scientific research. A femtosecond fiber chirped pulse amplification (FCPA) system operating at 1 μm is reported. This system consists of a 1.5 μm all-fiber passive mode-locked laser source, a 1 μm nonlinear frequency converter, a two-stage Yb-doped amplifier, and a transmission diffraction grating pulse compressor. The center wavelength of the erbium-doped mode light source is 1.55 μm, the spectral bandwidth of 3 dB is 12.9 nm and the repetition frequency is 17.5 MHz. After power amplification, a 9.5 cm high nonlinear fiber is injected to generate 1 μm band dispersion wave with center wavelength of 1070 nm and 3 dB spectral bandwidth of 33 nm. Moreover, using this dispersion wave pulse as the seed source, the pulse output with repetition rate of 1.09 MHz is achieved by using a frequency selector of acousto-optic modulator. After that, the power is amplified to 11.4 W, and with the femtosecond pulse laser output with average power of 7.7 W, spectral bandwidth of 21.4 nm at 10 dB, pulse duration of 270 fs, and peak power of 26 MW is achieved after compression.