Tunable Diode Laser Absorption Spectroscopy (TDLAS) has been widely applied in in situ and real-time monitoring of trace gas concentrations. In this paper, an advanced TDLAS-based optical gas sensing system with laser linewidth analysis and filtering/fitting algorithms is proposed and experimentally demonstrated. The linewidth of the laser pulse spectrum is innovatively considered and analyzed in the harmonic detection of the TDLAS model. The adaptive Variational Mode Decomposition-Savitzky Golay (VMD-SG) filtering algorithm is developed to process the raw data and could significantly eliminate the background noise variance by about 31% and signal jitters by about 12.5%. Furthermore, the Radial Basis Function (RBF) neural network is also incorporated and applied to improve the fitting accuracy of the gas sensor. Compared with traditional linear fitting or least squares method (LSM), the RBF neural network brings along the enhanced fitting accuracy within a large dynamic range, achieving an absolute error of below 50 ppmv (about 0.6%) for the maximum 8000 ppmv methane. The proposed technique in this paper is universal and compatible with TDLAS-based gas sensors without hardware modification, allowing direct improvement and optimization for current optical gas sensors.