The acoustomagnetoelectric (AME) effect in a superlattice (SL) is investigated for an acoustic wave whose wavelength $\lambda =2\pi/q$ is smaller than the mean free path $l$ of the electrons and hypersound in the region $ql\gg1$ (where $q$ is the acoustic wave number) . The analytical expression for the AME current $j^{AME}$ is calculated in the case of relaxation time of momentum $\tau$ is constant approximation. The result indicates that the existense of $j^{AME}$ in a SL may be due to the finite gap band , and the periodicity of the electron spectrum along the SL axis. Numerical calculations have been done and the result is analysed for the GaAs/AlAs SL. All the results are compared with the normal bulk semiconductors (both theory and experiment) in the weak magnetic field region to show the difference.
