Stimulated Brillouin scattering (SBS) effect is the main factor limiting the maximum output power of the continuous single frequency fiber laser. In order to suppress SBS effect in the gain fiber, a method is proposed which can broaden Brillouin gain spectrum, reduce Brillouin gain coefficient of the gain fiber, and thus improve the output power of the fiber laser by changing the doping concentration of the gain fiber. Based on the rate equation, thermal conduction and Brillouin gain spectrum calculation models, the thermal distribution of the gain fiber, the output power of laser and Brillouin gain spectrum are simulated under the conditions of constant and gradient doping when the maximum temperatures of the gain fibers are basically the same. Results show that, compared with the conventional constant doping fibers, the designed gradient doping gain fiber can broaden Brillouin gain spectrum by 1.2 times, reduce Brillouin gain coefficient by 41% and increase the SBS threshold power by 1.7 times, which suppresses the optical SBS effect effectively. The fusion point temperature of the gain fiber is reduced, and the stability of the fiber laser is improved.