Wavelength-swept laser is the key component for optical fiber sensing and optical coherence tomography, and its output spectral characteristics determine the resolution of the sensing and imaging systems.An improved heterodyne method and a direct measurement method by fast synchronous time gating with an electro-optic modulator (EOM) are proposed to dynamically measure the output spectra of a selfmade prototype of a ring cavity wavelength swept laser. The spectral linewidth, hence the coherence length of the laser source, are obtained to show its increasing dependence on the wavelength-swept frequency. The linewidth measured by the EOM method is greater than that of the heterodyne method due to the modulation, and the respective linewidth are 37 pm and 4.9 pm while the wavelength-swept frequency is 60 kHz.