A nonuniform large mode area fiber having an larger core at most locations to reduce power intensity and having a relatively smaller core at certain locations to reduce bending sensitivity is proposed for suppression of stimulated Brillouin scattering (SBS) in a high power fiber amplifier. A comprehensive model taking into account fiber nonuniformity, profile and temperature gradient shows that the fiber can achieve kilowatt output at a temperature gradient of >250 degrees C. Compared with a conventional large mode area fiber, a total of 7 dB SBS suppression can be achieved using this unique fiber.