Regarding to the problem that the backward amplified spontaneous emissions (ASE) in Tm-Ho co-doped fiber amplifier reduce the amplification efficiency beyond 2 μm band, the influence on gain property beyond 2 μm band by inserting a 1950 nm fiber Bragg grating (FBG) into the input terminal of the amplifiers with different Tm/Ho doping ratios is studied theoretically. Simulation results of the 2040 nm signal gain over the fiber length with or without FBG are given under several different Tm/Ho doping ratios in order to analyze the variations of maximum gain and corresponding optimal fiber length due to the insertion of FBG, as well as the dependence of the variations on Tm/Ho doping ratio. The influence of FBG is explained through simulating the backward ASE spectrum at z=0, and the propagation of pump, signal, ASE and reflected light from FBG along the fiber. Discussions on the simulation results further point out the applicable conditions of short-band FBG for improving long-band gain of amplifier. In addition, the influences on gain spectrum and noise characteristics by FBG are also investigated.