In this paper, we studied the dynamics of a dispersion-tuned swept-fiber laser both experimentally and theoretically. By adding a dispersion compensation fiber and an electro-optic modulator in the laser cavity, an actively mode-locked laser was obtained by using intensity modulation, and wavelength sweeping was realized by changing the modulation frequency. Using a high-speed real-time oscilloscope, the dynamic behaviors of the swept laser were investigated during wavelength switching, static-sweeping cycle, and continuous sweeping, respectively. It was found that the laser generates relaxation oscillation at the start of the sweeping mode. The relaxation oscillation process lasted for about 0.7 ms, and then the laser started to operate stably. Due to the nonlinear effect, new wavelengths were generated in the relaxation oscillation process, which is not beneficial for applications. Fortunately, relaxation oscillation disappears if the laser starts up and operates in the continuous sweeping mode, and the good sweeping symmetry between the positive sweep and negative sweep increases the application potential of the laser. In addition, the instantaneous linewidth is almost the same as that in the static state. These results describe the characteristics of the laser from a new perspective and reveal, to the best our knowledge, the intensity dynamics of such lasers for the first time. This paper provides some new research basis for understanding the establishment process of dispersion-tuned swept-fiber lasers and their potential application in the future.