In this work, we propose a high-efficiency terahertz (THz) wave-generation approach by cascaded difference frequency generation (CDFG) with an aperiodically poled lithium niobate (APPLN) crystal at cryogenic temperature. The APPLN crystal with desirable poling periods along the crystal length determines phase mismatches of each-order CDFG, resulting in a decrement of phase mismatches in cascaded Stokes processes and an increment of phase mismatches in cascaded anti-Stokes processes simultaneously. This is in contrast with previous works on CDFG, where the THz wave was generated with irreversible phase mismatches in cascaded Stokes and anti-Stokes processes. The variations of phase mismatches enhance the evolution of optical spectra in cascaded Stokes processes and restrain the evolution of optical spectra in cascaded anti-Stokes processes, yielding unprecedented energy efficiencies in excess of 30% from optical waves to THz waves with APPLN. The unprecedented energy efficiencies in this work are theoretical results without THz wave absorption at a temperature of 10 K. Compared with the maximum THz intensity from traditional CDFG using periodically poled lithium niobate, the maximum THz intensities are enhanced by 2.5 and 2.8 times using APPLN with stepwise changing and gradually changing poling periods, respectively.