We numerically demonstrate a simple one-dimensional model of an acoustic diode formed by coupling a superlattice with a strongly nonlinear medium. The first numerical observation is presented of a significant rectifying effect on the acoustic energy flux within particular ranges of frequencies. By studying the underlying rectifying mechanism and the parameter dependence of the rectifying efficiency, the effectiveness of the acoustic diode is proved despite its simplicity. We also briefly discuss possible schemes of the experimental realization of this model as well as devising more efficient models.