Heterodyne phase-sensitive dispersion spectrometer (HPSDS) retrieves the concentration of gas samples by measuring the refractive index fluctuations near the molecular resonance. Compared to previous HPSDS studies focusing on pure intensity modulation, it is attractive to investigate the performance of HPSDS sensor based on a distributed feedback (DFB) laser under conditions where frequency modulation is much higher than intensity modulation. In this work, we report the implementation of a near-infrared HPSDS for methane detection based on the direct modulation of a DFB laser. The performance of our HPSDS is assessed using the characteristic absorption peak of methane near 1653.7 nm. Long-time measurements show that our HPSDS has a detection limit (MDL) of 1.22 ppm at standard atmospheric pressure and room temperature. In the same experimental conditions, we have experimentally compared HPSDS to wavelength modulation spectroscopy (WMS) to evaluate the dynamical range, long-term stability, and precision limits of the two methods.