To simulate the periodic and weak vibration in the fiber sensor application, a loop-cavity fiber laser of the periodic frequency sweeping is constructed by tuning the fiber Bragg grating (FBG). To measure the sweeping frequency, the optical frequency multiplication is applied with the help of fiber Bragg grating Fabry-Perot cavity. This fiber laser has experimentally radiated a 7.2 Hz frequency-swept laser and 14.39 Hz electric signal is obtained by the frequency multiplication method. The experimental results show that this system can efficiently simulate the periodic frequency-swept light wave and exactly measure the sweeping frequency.