We have demonstrated a simple method for achieving broadband amplification and short-pulse generation in a polarizing maintained (PM) Yb fiber amplifier with the implementation of a narrow bandpass filter (NBF). By using an NBF with a spectral bandwidth of 3.3 nm at a wavelength of 1036 nm before the PM Yb amplifier, the spectral bandwidth was extended by self-phase modulation (SPM) in the PM YDF amplifier. The recompressed pulse duration of 125 fs obtained with the NBF was nearly three times shorter than that (350 fs) achieved without the NBF, and therefore the peak intensity of 0.35 MW with the NBF was over two times greater in comparison with that (0.16 MW) obtained without the NBF. We believe that this simple method is useful for developing an all-fiber laser system for high-power short pulse generation.