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We have realized a novel tunable narrow linewidth fiber laser with single-longitudinal-mode operation based on the homogenous gain broadening effect of Er-doped fiber and the stimulated Rayleigh scattering (STRS) in a nonuniform optical fiber in a ring laser configuration. A 3 dB linewidth of less than 2.0 kHz is achieved with 70 dB extinction. The minimum tunable laser bandwidth is determined by the balance of the bandwidth of tunable bandpass filter (in GHz), relaxation time and gain of the Er-doped fiber, and cavity loss. The tuning range is determined by the range of tuning filter within Er-doped fiber gain spectrum. This technique is applicable to any fiber with much higher stimulated Brillouin scattering threshold than that of STRS.