In order to explore the comprehensive characteristics of the linewidth of the lasers, the theoretical analysis of the linewidth of the wavelength-tunable narrow linewidth lasers is carried out. In this paper, the delayed self-heterodyne measurement system based on the non-equilibrium Mach-Zehnder interferometer structure is built to investigate the steady-state and dynamic linewidth characteristics of wavelength-tunable narrow linewidth lasers. In order to balance the speed and accuracy of linewidth measurements, linewidth tests at different receiver bandwidths are implemented. For the linewidth spreading problem arising from continuous laser wavelength tuning, the linewidth measurement error is compensated by controlling the stepping amount while maintain the stability of the output power. This study can not only improve the study of laser linewidth characteristics, but also has important significance for the study of optical frequency-domain reflectometry technology.