It is quite urgent to need a flexible photodetector in the ultraviolet-visible-near infrared region for building a miniaturization broadband spectrometer. In the present paper, one kind of flexible black silicon doped with sulfur and fluorine was proposed and the optical absorption spectrum was investigated in broadband region. Firstly, the electronic structure, band structure and the optical absorption properties of the flexible black silicon doped with sulfur and fluoride were calculated using the first-principles pseudo potential calculations based on density-functional theory. Then, the absorption spectrum model of the flexible black silicon was built based on both the first-principles and finite domain time difference method. The results show that the cut-off wavelength has a red shift as the band gap of doped material becomes narrower. The higher the doping concentration is, the higher the optical absorption coefficient is obtained. The absorption coefficient of flexible black silicon doped with 50% sulfur is 8.3 times higher than that of 1.5% sulfur doping sample at the wavelength of 1 500 nm while the ratio turns to be 3 times when doped with 50% and 1.5% fluoride. The black silicon with small-size surface microstructure has the highest absorptance in the near-infrared region at the same doping concentration of 50%. Finally, a sample of flexible black silicon was fabricated by the femtosecond laser auto scanning system. The test results indicate that the absorptance of the sample is higher than 95% both in the ultraviolet and visible region and is fluctuated from 70% to 80% in the near-infrared region. It shows that as a novel light-absorbing material in broadband region the flexible black silicon doped with Sulfur and Fluorine has an potential application in exploring miniaturization broadband spectroscopy.