Output beam characteristics of a LD-pumped multimode graded-index fiber Raman laser with different cavity configurations are studied. It has been shown that specially designed 976-nm FBGs inscribed by femtosecond pulses enable selection of an individual transverse mode: Fundamental LP01 mode is generated in case of FBG localized in the center of graded-index fiber core, whereas next-order LP11 mode is generated in case of FBG shifted by ∼8 um from the center. Corresponding beam shapes and spectra are observed in the laser output. At that, output power at the same pumping is sufficiently higher in case of LP11 FBG. Optimization of output characteristics is also performed resulting in generation of ∼50 W power at 976 nm with beam quality parameter M22.