We report a wavelength swept fiber laser at the 1 μm region based on an actively mode-locked dispersion-tuning technique. The ring-cavity laser uses a 70 cm ytterbium-doped fiber as a gain medium. Mode locking is achieved by the direct modulation of the amplitude modulator, and a $～1000\mathrm{m}$ single-mode fiber is used to provide the desired intracavity dispersion. By sine-modulating the modulation frequency, a wavelength swept laser with a range of $～30\mathrm{nm}$ can be achieved at a sweeping rate of 50 Hz. The characteristics of the laser, such as its single-wavelength tuning range, tuning sensitivity, static linewidth and sweeping rate, are also studied experimentally.