Abstract: Ultrasonic transducers have widely been used in industrial non-destructive detection, medical diagnosis, and other fields of applications. With the development of technology and broadening and deepening applications, there is a constant need of higher performance transducers, e.g., for higher resolution imagining, etc. To break through the bandwidth limit of traditional ultrasonic transducers that are based on the quarter-wavelength matching, novel impedance matching technology has to be developed. Following the acoustic wave equation in inhomogeneous media, we study the transmission spectrum of continuous media of gradiently varying acoustic properties, and then, explore the possibility of using tubes of variable cross-section and multi-layered media to realize the equivalent gradient media with their matching performance well agreeing with those of the gradient media. Numerical simulations of the performance of transducers with two, three, and four matching layers are conducted by using the finite element method to attain optimized parameters of matching layers.