An all fiber Yb 3+ doped fiber laser based on fiber Bragg gratigns (FBG) is presented.The laser output at 1 060 nm with a spectrum brand width of 0.14 nm is obtained when pumped by a laser diode (LD) at 978 nm.The resalts shown that the laser threshold and output power changed with the length of the Yb 3+ doped fiber,but the spectrum band width is unchanged.The maximum output power is 2.36 mW,and the slope efficiency is up to 22.2 %.