In this paper, we report 38.8 W average power output through a single-stage fiber amplifier, with emission of 1064 nm wavelength with 80 MHz repetition and 35 ps pulse width amplified from a 2.15 W SESAM passively mode-locked Nd:YVO4 laser oscillator. The high power fiber amplification is through a coupled 60.8 W 976 nm backward unidirectional pump power into a 2 m long 30/250 μm Yb-doped inner cladding. No obvious nonlinear effects arise in the high power output. To our knowledge this is the highest average power output with 2 m 30/250 μm Yb-doped double-clad fiber in a single-stage picosecond fiber amplifier.