A novel kind of fiber amplifier——quantum dot doped fiber amplifier (QDFA) is presented. Using semiconductor nanocrystal PbSe as a dopant, the gain bandwidths of the PbSe-QDFA are simulated by solving the rate equation and the light propagation equation in a two-level system, applying a genetic algorithm combined with an “inversing method”. Comparing with conventional erbium-doped fiber amplifiers available, there is evidence to show that characteristics of the PbSe-QDFA are obviously advantageous in respect of bandwidth and noise, especially on long-waelength band. Furthermore, the ideal emission-absorption cross-sections of the quantum dot are determined by utilizing the genetic algorithm. Under such ideal cross-sections, the QDFA possesses with the performance of ultra-bandwidth and low noise figure near a quantum limit.