Detailed theoretical analysis of the gain characteristics of quantum-dot semiconductor optical amplifiers (QD-SOA) is presented. An analytical expression for the optical gain is derived from the quantum dot and wetting layer rate equations. Due to the better confinement of carriers in the quantum dots, our calculation shows that large unsaturated optical gain can be obtained at low operating current. Also, we found that the output saturation intensity of QD-SOA is higher than the output saturation intensity of bulk-SOA. This fact lends itself to the design of efficient low-power SOAs.