In research field of optics, diffraction gratings are widely investigated and applied; on the other hand, periodic metal waveguide is familiar to those worked with microwave waveguide. The early studies on periodic waveguide have a profound impact on the development of the waveguide optics. Currently, periodic waveguide has become an important integrated optical element and obtains a wide range of applications in functional devices such as the grating couplers, filters, distributed feedback lasers, and the distributed Bragg reflector lasers. The most common analysis method on the periodic waveguide is the coupled mode theory (Yariv in Quantum electronics. Wiley, New York, 1975), which is extremely effective to deal with the coupling between different modes. However, the method is cumbersome in mathematics and lack of clearness in giving physical insight. In this chapter, we introduce another method (viz. the transfer matrix method) to analyze the periodic waveguide. The simple rectangular periodic waveguide is discussed first, and then, the periodic waveguide of arbitrary shape is also studied.