The cw pumped self-staring,widely tunable ps pulses Yb~(3+)-doped double-clad fiber laser is experimentally studied.In experiments,the 20 m single mode Yb~(3+)-doped double-clad fiber worked as gain medium.And we used 77 MHz RF signal AOM and a grating which formed external cavity to provide feedback,and made the laser linewidth narrower.We obtained 1 GHz repetition rate with highest output power 56.3 mW pulses,whose width was smaller than 60 ps.Also,the fiber laser was tunable over 40 nm from 1 072.9 nm to 1 113.7 nm.