Using a transfer matrix method, we investigate the transmission property of the acoustic-phonon modes in symmetrical multilayer heterojunctions consisting of many different heterojunctions (GaAs/AlxiGa1-xiAs) within elastic continuum approximation. Our results show that the oscillation amplitude and frequency are different between transmission curve in such structure and transmission curve in the superlattice (GaAs/AlAs) with the same thicknesses of constituent layers. The features of transmission spectrum are influenced by the distribution of the concentration xi(i denotes the i th AlxiGa1-xiAs slab on both sides of the symmetrical axis) . When the concentration xi in AlxiGa1-xiAs slab decreases with the increase of i, the curve in transmission spectrum is flat except in the vicinity of the main valley. When the concentration xi increases with the increase of i, the oscillation amplitude of the curve increases and the main valley is split. Our results also show that the transmission coefficient is sensitive to the thicknesses of constituent layers, especially the thickness of AlxiGa1-xiAs. In addition, it is found that the number of heterojunctions influences the transmission of acoustic phonon.