A common-path dual-wavelength phase demodulation technique for extrinsic Fabry-Perot interferometric (EFPI) sensors is proposed on the basis of a broadly tunable modulated grating Y-branch (MG-Y) laser. It can address the three main concerns of existing dual-wavelength phase interrogation methods: the imbalances and disturbances caused by two optical paths utilizing two lasers or two photodetectors, the restrictions between two operating wavelengths and the cavity length of EFPI, and the difficulty in eliminating the direct current (DC) component of the interferometric fringe. Dual-wavelength phase interrogation is achieved in a common optical path through high-speed wavelength switching. Taking advantage of the MG-Y laser's full spectrum scanning ability (1527 ∼ 1567 nm), initial cavity length and DC component can be directly measured by white light interferometry. Two quadrature wavelengths are then selected to perform high speed phase demodulation scheme. Three polyethylene terephthalate (PET) diaphragm based EFPI acoustic sensors with cavity lengths of 127.954 µm, 148.366 µm and 497.300 µm, are used to demonstrate the effectiveness.