Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation and because PC-based waveguides may be integrated into optical interferometers. We propose a novel tunable PC waveguide Mach-Zehnder interferometer based on nematic liquid crystals and investigate its interference properties numerically by using the finite-difference time-domain method. We can change the refractive indices of liquid crystals by rotating the directors of the liquid crystals. Then we can control the phase of light propagation in a PC waveguide Mach-Zehnder interferometer. The interference mechanism is a change in the refractive indices of liquid-crystal waveguides. The novel interferometer can be used either as an optically controlled on-off switch or as an amplitude modulator in optical circuits.