The measurement of a laser linewidth is significant in metrology, coherent optical communications, high-resolution sensing, and LIDAR. Firstly, in this study, we theoretically explain why estimating an integrated linewidth via a frequency-noise power spectral density (PSD) is valid. We find that the previous methods estimating the integrated linewidth via the frequency-noise PSD result from Gaussian approximation and obtain a more general consequence. Secondly, according to the theory, we propose the Voigt approximation method to improve the estimation performance. The simulation results show the Voigt approximation estimation error is lower than 5%. Finally, based on the Voigt approximation, the relationship between the interference visibility and laser linewidth is found, providing a possible convenient approach to measuring the linewidth.