To address the measurement errors introduced by laser linewidth in the traditional swept-frequency methods, a signal analysis approach based on convolution fitting is proposed, leveraging the convolutional characteristics of Guassian-shaped laser spectrum and Lorentzian-type Fabry-Perot (F-P) cavity. An swept-frequency optical fiber experimental platform is constructed to verify the performance of the two F-P cavities (one is custom-built (Cavity 1) and another is commercial (Cavity 2)) . Firstly, the impact of laser linewidth on the signal profile is quantified through simulations, and the main process of the fitting algorithm is introduced. Secondly, the spectrum of the incident laser is measured via beat-frequency analysis. The experimental results indicated that the spectrum exhibited a Gaussian shape with a linewidth of (11.59 ± 1.23) kHz. Subsequently, the frequency modulation error of the swept-frequency platform is evaluated. Linewidth measurements are conducted on the cavity 1 and cavity 2 using the swept-frequency method. For Cavity 1, the results of Lorentzian fitting and convolutional fitting are (204.1 ± 11.2) kHz and (203.9 ± 11.2) kHz, respectively, showing no significant difference. For Cavity 2, which had a calibrated linewidth of 4.17 kHz, the result of Lorentzian fitting is (8.97 ± 0.42) kHz, while the result of convolutional fitting is (4.42 ± 0.50) kHz. The experimental results demonstrate that when the laser linewidth is comparable to the cavity’s linewidth, this method can accurately measure the true linewidth of the cavity. When the laser linewidth (11.59 kHz) is significantly smaller than the cavity’s linewidth (204.1 kHz), the results obtained using this method are similar to those from the Lorentzian fitting approach. This work broadens the range of options for selecting linewidth measurement equipment for narrow-linewidth Fabry-Pérot (F-P) cavities.