A random distributed feedback fiber laser with linear polarized output at 1178 nm is presented. Linear polarization is realized by fiber coiling in a half-opened cavity of a polarization maintaining random fiber laser structure. The single linear polarization laser output power reaches ～3 W with polarization extinction ratio >14 dB. Further investigations on the coiling technique and additional feedback are also studied. So far as we know, this is the first reported linear polarized random distributed feedback Raman fiber laser.