A large swept-range wavelength-swept Er-doped fiber laser based on dispersion tuning is reported. By introducing large dispersion in the cavity of the active mode-locked laser, the output wavelength can be swept through changing modulation frequency. The laser can be applied to fiber Bragg grating (FBG) sensing. When the output light of the wavelength-swept laser is reflected by FBG, the variation of FBG central wavelength induced by strain can be converted into different time delays of signals. The output characteristics of the wavelength-swept laser are experimentally studied. The wavelength-swept range is 43 nm approximating the gain bandwidth of Er-doped fiber, while the sweep rate is 50 Hz. The principle of this demodulation technique is demonstrated and the sensitivity is about 0.68 ms/nm.