The matching layers prepared by the conventional λ/4 (λ is the wavelength) resonant transmission matching technology can’t meet the high performance requirements in the current industry. In this paper, the acoustic propagation of two kinds of gradient impedance matching modelsof onedimensional variablegradient density material and variable crosssection waveguidesare studied theoreticallyand the acoustic energy transmittance of impedance gradient graded material is derived.Then the variable crosssection waveguides with a variety of shapes are numerically simulated, and the effects of matching layer thickness and crosssection shape on the transmittance are analyzed. The numerical simulation results show that the matching layer with variable crosssection waveguides has all transmission performance at high frequency acoustic intensity and the thicker the matching layer, the lower the lowfrequency cutoff frequency. The performance of the ultrasonic transducer can be improved by using the proposed matching layer with variable crosssection waveguides.