A PbSe quantum-dot-doped fiber amplifier (QDFA) in NIR region is realized in the experiment. We fabricate the PbSe quantum dot fiber (QDF) with the central diameter of 4.08-5.88 nm by optimizing the heat treatment conditions of the melt-annealing method in the sodium-aluminum-borosilicate silicate glass. The QDFA is composed of the QDF, the wavelength division multiplexer, the isolator, and the pump laser. The experimental results show that the signal light is amplified in the gain wavelength range of 1260-1380 nm depending on the particle size of quantum dots, where signal gain is 16.4 dB and -3 dB bandwidth reaches to 80 nm for the input signal of -17 dBm. An obvious excitation threshold and gain saturation phenomenon are observed in the experiment. Compared with conventional erbium-doped fiber amplifiers and few-mode erbium-doped fiber amplifiers, the proposed QDFA has a lower excitation threshold, wider bandwidth, and lower noise. It provides a novel approach to extend the current optical-fiber-communication waveband and industrial applications.