655 nm laser radiation with power of >60 mW is generated by frequency doubling of a broadband randomly-polarized 1.31-microm Raman fiber laser (RFL). The red power appears to grow linearly with increasing RFL power up to 7 W at efficiency comparable with that for single-frequency lasers. It has been shown that multiple sum-frequency mixing processes involving different RFL modes provide the main contribution to the output, which is enhanced by 2 times due to the modes stochasticity.