The spectrum function of an active fiber ring resonator was obtained through simple theoretical analysis, which clearly point out the frequency filtering characteristics of active fiber ring resonators. Based on this formula, the effects of the linewidth of input laser and the parameters of an active fiber ring resonator on the output linewidth were discussed. To confirm these theoretical results, some experiments were designed using different input laser and different active fiber ring resonators. All the theoretical and experimental results indicated that the free spectral range (FSR) of an active fiber ring resonator and the linewidth of input laser directly affect the spectral-shape and output linewidth of the ring because of the multi-peaks response of active fiber ring resonators' intensity transmitted function. For a ring with one peak output, the output linewidth is affected together by the input linewidth and the instinct linewidth of the ring, which induced that the output linewidth is narrower than the instinct linewidth.While for the one with multi-peaks output, the output linewidth is close to the instinct linewidth of the ring.Therefore using the optical fiber amplifier to compensate the round trip loss of an active fiber ring resonator,narrower linewidth laser output can be obtained.