A wavelength-swept fiber laser is proposed and successfully demonstrated based on a bidirectional used linear chirped fiber Bragg grating (LC-FBG). The wavelength-swept operation principle is based on intracavity pulse stretching and compression. The LC-FBG can introduce equivalent positive and negative dispersion simultaneously, which enables a perfect dispersion matching to obtain wide-bandwidth mode-locking. Experimental results demonstrate a wavelength-swept fiber laser that exhibits a sweep rate of about 5.4 MHz over a 2.1 nm range at a center wavelength of 1550 nm. It has the advantages of simple configuration and perfect dispersion matching in the laser cavity.