A magnetostrictive /elastic substrate /piezoelectric composite has been developed where the elastic substrate takes the form of trapezium to amplify the strain. By using the equivalent circuit, the magnetoelectric response of the composite in the longitudinal vibration has been analyzed. The magnetoelectric response of a Terfenol-D/trapezoidal Be-bronze/PZT-5H composite is calculated and is compared with the experiment. It is indicated that the theoretical response shows a similar variation tendency as the experimental in spite of the difference in resonant frequencies and the values of the magnetoelectric voltage coefficients, which is the result of neglecting the glue behavior. At the same time, the composite on a trapezoidal substrate and the composite on a rectangular substrate are compared, which indicates that the former has higher magnetoelectric voltage coefficient. The length ratio of the trapezoidal elastic substrate and the thickness ratio of the composite are further analyzed. It is found that the composite will have maximum magnetoelectric voltage coefficient when: (1) the ratio of the length of wide section to the total length of a trapezoidal elastic substrate is 0.45; (2) the thickness of a trapezoidal elastic substrate is one fourth that of Terfenol-D layer.