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In this work, a pulsed wavelength-tunable Brillouin fiber laser based on a Fourierdomain mode-locking (FDML) source with a repetition rate of 4.2 kHz is presented. The tunable Brillouin laser is formed by a fiber-ring cavity (for the Stokes signal amplification) within a primary fiber-ring cavity for generating an FDML signal. The primary cavity is formed by an erbium-doped fiber amplifier and a fiber Fabry-Perot filter (FFP-F) as the gain medium and the tunable optical bandpass filter, respectively. A spectral laser tuning range of 2.54 nm centered in 1531 nm was achieved by adjusting the offset voltage of the FFP-F, while a variation, from 0.282 to 0.462 nm, on the Brillouin linewidth of the laser was achieved by setting the amplitude of a modulation signal applied in the FFP-F. A laser pulsewidth of 6.50 μs was measured, and an output power of -7 dBm was achieved.