Subject to the poor imaging quality of the infrared camera, the projector defocusing, and the subsurface scattering, the classical phase-shifting method is constrained for reconstructing three-dimensional (3D) face geometry. To address this issue, a face measurement method based on stripe edge detection using infrared light is proposed by designing the global codeword correction. Binary fringe instead of sinusoidal fringe is employed to resist the above disturbance. Significantly, an assistant fringe is developed according to the parity of the gray order, which then is utilized to generate the correction orders. Subsequently, the correction orders are employed to guide the decoding by the discriminator of the rising and falling edges in binary patterns. In this way, the 3D face without jump errors can be reconstructed using an infrared structured light system. Experiments verify the effectiveness of our method not only on the human face but also on the standard sphere and models.