A whole-fiber methane sensor under high absorbance based on phase sensitive chirped laser dispersion spectroscopy is presented in this paper. The laser source of the sensor is a tunable distributed feedback diode laser with a frequency of 1653.7 nm. A telecom-based electro-optical intensity Mach-Zehnder modulator working in carrier suppression mode is adapted to modulate the single frequency laser beam for generating a dual-sideband spectrum beside the carrier wave. Unlike previous proposed phase sensitive chirped laser dispersion spectroscopy scheme, the beatnote signal generated by the two sidebands is detected experimentally. The refractive index fluctuation around the 23 transition of methane is measured by detecting the phase variation of the dual-sideband beatnote signal through using the heterodyne interferometric method. A lock-in amplifier is employed in the phase demodulation process. By connecting the refractive index (the real part of the complex refraction index) and the absorption coefficient (the imaginary part of the complex refraction index) via Kramers-Kroning relation, the gas concentration information is retrieved from the optical dispersion measurement. Absorption-based wavelength modulation spectroscopy measures the gas concentration encoded in the optical intensity based on Beer-Lambert's law. However, the signal sensitivity of wavelength modulation spectroscopy decreases, and the signal even decreases while the gas concentration is raised in high absorbance condition, which leads to an uncertainty in concentration measurement. Experimental results demonstrate that wavelength modulation spectroscopy has better performance in low absorbance condition. The detection limit is about 38.1 ppmm. However, because the sensitivity decreases in high absorbance conditions, the upper detection limit of wavelength modulation spectroscopy is only 1500 ppmm. The dynamic range is defined through dividing the upper detection limit by the detection limit. Therefore, the wavelength modulation spectroscopy obtains a linear measurement dynamic range of 16 dB. Nevertheless, under the same experimental condition, the phase sensitive chirped laser dispersion spectroscopy has a much larger linear measurement range from 47.3 ppmm to 174825 ppmm with a dynamic range higher than 35 dB. Absorption-based gas measurement technique such as wavelength modulation spectroscopy can achieve a low detection limit by using long optical path at the expense of lower upper limit concentration. Phase sensitive chirped laser dispersion spectroscopy appears to be effective in high absorbance condition, which may be caused by high concentration or long optical path. Furthermore, by combining phase sensitive chirped laser dispersion spectroscopy and long optical path technique such as multi pass cell in sensor design, large linear measurement dynamic range and low detection limit can be obtained at the same time.