We propose a precision phase-generated-carrier (PGC) demodulation method with sub-nanometer resolution that avoids nonlinear errors in a laser wavelength sinusoidal modulation fiber-optic interferometer for long range dynamic displacement sensing. Using orthogonal detection and an AC-DC component extraction scheme, the PGC carrier phase delay (CPD) and laser intensity modulation phase delay can be obtained simultaneously to eliminate the nonlinear error from accompanied optical intensity modulation and CPD. Further, to realize long range displacement sensing, PGC phase modulation depth (PMD), determined by the laser wavelength modulation amplitude and the working distance of the interferometer, is required to maintain an optimal value during measurement, including initial position and dynamic movement. By combining frequency sweeping interference and modified PGC-arctan demodulation to measure real-time working distance, adaptive PMD technology is realized based on proportion control. We construct a fiber-optic Michelson and SIOS commercial interferometer for comparison and perform experiments to verify the feasibility of the proposed method. Experimental results demonstrate that an interferometer with sub-nanometer resolution and nanometer precision over a large range of 400 mm can be realized.