The experimental study on transmission characteristics of high-peak power laser pulses with width of 5 ns and wavelength of 1064 nm via all-silica fibers with core diameter of 600 μm are demonstrated. According to N-ON-1 test mode,the laser induced fiber damage threshold and transmission efficiency curve are obtained. The 50% probability damage threshold is 24 mJ,the average output energy is 14 mJ,and the peak power approaches to 3 MW. The three processes of fiber delivery high-peak power laser pulsed are presented,which are undamaged stage (steady state),laser-induced plasma stage (unsteady state) and laser-induced fiber core damage stage (transmission cut-off). The damaged morphologies and damage mechanism are investigated. The synchronous increases of laser induced plasma threshold and entry damage threshold can improve optical fiber capability for high power laser delivery.