In this paper, we demonstrate a narrow linewidth random fiber laser, which employs a tunable pump laser to select the operating wavelength for efficiency optimization, a narrow-band fiber Bragg grating (FBG) and a section of single mode fiber to construct a half-open cavity, and a circulator to separate pump light input and random lasing output. Spectral linewidth down to 42.31 GHz is achieved through filtering by the FBG. When 8.97 W pump light centered at the optimized wavelength 1036.5 nm is launched into the half-open cavity, 1081.4 nm random lasing with the maximum output power of 2.15 W is achieved, which is more powerful than the previous reported results.