Introducing the gain competition is an effective way to suppress stimulated Brillouin scattering (SBS) in single frequency fiber amplifier. Steady rate equation describing two-tone single frequency Yb-doped double cladding fiber amplifier with gain competition is deduced based on single frequency amplifier. A theoretical model of this kind of amplifier is set up. With this model, simulation is performed to analyze the influences of wavelength difference between signals, signal power ratio, pump configuration and length of gain fiber on output efficiency of single frequency laser, and the effect of SBS suppression.