As widely used in military, medicine, communication, processing and other fields, femtosecond laser has become a research hotspot of the whole laser technology in the 21st century. The pump source used by laser diodes (LDS) has become a new development trend of all-solid-state femtosecond lasers owe to the rapid development of LDs. Yb^3＋-doped laser crystal materials gradually become important gain media for LD pumping and generate 1.0 μm femtosecond laser due to their unique energy level structures, broad absorption and emission spectra. In this paper, the research progress of Yb^3＋-doped femtosecond laser crystals is summarized in detail, the main problems are analyzed, and two directions for the development of femtosecond laser crystals in the future are proposed: high efficiency and low power femtosecond laser, high power and high energy femtosecond laser. The crystal growth, spectra properties, continuous and femtosecond laser performances of the Yb^3＋:Sr₃Y₂(BO₃)₄ crystal were studied in detail. And the Yb^3＋:Sr₃Y₂(BO₃)₄ femtosecond laser with the center wavelength of 1060 nm, pulse width of 116 fs, average output power of 1.08 W and optical conversion efficiency of 33.1% were successfully generated. The experimental results indicate that Yb^3＋:Sr₃Y₂(BO₃)₄ and its corresponding system crystals are excellent femtosecond laser materials with high optical conversion efficiency.