In this paper, we developed a dual-sideband beat-suppressed heterodyne phase-sensitive dispersion spectroscopy (HPSDS) for sensitive detection of trace gases across a wide dynamic range and explored the operational characteristics of the electro-optic modulator (EOM) and bias voltage control methods under sideband suppression mode. The dispersion phase spectral profiles and the corresponding signal-to-noise ratios in both suppression and non-suppression modes were compared before a comprehensive evaluation of the detection performance. A HPSDS-based detection system was developed based on a near-infrared distributed feedback laser and an EOM. The suppression of the dual-sideband beat was achieved by exploring and analyzing the optimal operational range of the EOM, leading to the optimization of dispersion phase signals with increased amplitude and high signal-to-noise ratio. The dispersion phase signals under typical high-frequency (1.2 GHz) intensity modulation were recorded for different standard methane/nitrogen mixtures. The relationship between the peak-to-peak values of the dispersion phase signals and the varied gas concentrations was then summarized. Meanwhile, wavelength modulation spectroscopy (WMS) experiments were conducted; subsequently, the HPSDS and WMS techniques’ performances were compared in terms of linearity, dynamic detection range, and immunity to optical power fluctuations. Finally, the HPSDS-based system's performance under a wide dynamic range and rapid time response was verified by measuring different concentrations of standard gases. Experimental results indicate that the HPSDS technique exhibits high linearity (R² = 0.9999), a wide dynamic range (38.5 ppm to 40%), and remarkable immunity to optical power fluctuations. The dual-sideband-beat-suppression-HPSDS-based methane sensor developed in this paper shows great potential for applications involving wide dynamic range detection and on-site practical trace gas detection.