We demonstrate an L-band passively mode-locked femtosecond fiber laser with a fundamental repetition rate of 1.013 GHz based on a semiconductor saturable absorber mirror. Compared with other reported L-band fiber lasers that use overlong Er-doped fiber, the laser here consists of 10 cm heavily doped fiber to increase the fundamental pulse repetition rate to gigahertz level. An output ratio as low as 0.2% is used to make the central wavelength up to 1.6 μm. The laser operates at the soliton regime with a 3 dB spectral bandwidth of 13.6 nm and a pulse duration of 229 fs. © 2019 Optical Society of America.