We propose a novel tunable photonic crystal (PC) waveguide Mach-Zehnder interferometer (MZI) based on nematic liquid crystals (LCs) 5CB and investigate its interference properties numerically by using the finite-difference time-domain method. We can change the refractive index of LC by rotating the directors of the LC molecules. The line defect modes of the PC waveguide with different liquid crystal refractive indices are analyzed by using the plane wave expansion method. Owing to the slow group velocity region of the line defect mode, when the index of 5CB changes from 1.53 to 1.63, the variation of the effective index of the line defect mode arrives at 0.168. This property helps to significantly control the phase of light propagation in a PC waveguide MZI. The novel interferometer can be used as either an optically controlled on-off switch or an amplitude modulator in optical circuits.