Based on the rate equation, the amplification performance of small-mode-area (SMA) and large-mode-area (LMA) ytterbium-doped double-clad fiber amplifiers was studied using the finite-difference method. The Yb-doped double-clad fibers with the mode diameter 6.5 μm and 20 μm were used as the gain media for the amplification of narrow-band signals. Under the pump laser at the center wavelength of 915 nm, the relationships between output power and input signal power, pump power as well as fiber length, were discussed for SMA and LMA. Especially for LMA fiber amplifiers, it is important to choose the optimal fiber length. For the fiber amplifier with different mode diameters, the optimal pump power and fiber length were also analyzed. It is obtained that the critical pump power is about 4 W with the fiber length of 4 m, which is in accord with the experimental results. The results provide a theoretical guide to optimize fiber type and fiber length considering available signal and pump power, desired gain and mode requirement of fiber amplifiers.