A passive homodyne phase demodulation technique based on a linear-fitting trigonometric-identity-transformation differential cross-multiplication (LF-TIT-DCM) algorithm is proposed. This technique relies on two interferometric signals whose interferometric phase difference is odd times of π. It is able to demodulate phase signals with a large dynamic range and wide frequency band. An anti-phase dual wavelength demodulation system is built to prove the LF-TIT-DCM algorithm. Comparing the traditional quadrature dual wavelength demodulation system with an ellipse fitting DCM (EF-DCM) algorithm, the phase difference of two interferometric signals of the anti-phase dual wavelength demodulation system is set to be π instead of π/2. This technique overcomes the drawback of EF-DCM-that it is not able to demodulate small signals since the ellipse degenerates into a straight line and the ellipse fitting algorithm is invalidated. Experimental results show that the dynamic range of the proposed anti-phase dual wavelength demodulation system is much larger than that of the traditional quadrature dual wavelength demodulation system. Moreover, the proposed anti-phase dual wavelength demodulation system is hardly influenced by optical power, and the laser wavelength should be strictly limited to lower the reference error.