We report on the effects of spectral shaping of the output coupler fiber Bragg grating (OC-FBG) in a Yb-doped fiber laser on the laser emission spectrum for the purpose of inhabiting stimulated Raman scattering (SRS). The lasers with four different OC-FBGs were built and characterized. We found that the laser with a multiple reflection peak chirped-moiré OC-FBG produced a broad laser emission linewidth, which, in turn, led to about 100 times lower the SRS emission as compared with the laser with a 0.19 nm Gaussian-shaped OC-FBG. A nearly flat-top laser output spectrum was obtained from the lasers with a triangle-shaped and chirped-moiré OC-FBG, respectively.