The invention discloses an acoustic power multi-stage amplification traveling-wave thermoacoustic engine system, which consists of a loop structure formed by connecting N stages of thermoacoustic engine units end to end through resonant tubes and a load, wherein each unit is equal in length and unequal in cross sectional area; the units form a loop from large to small cross sectional areas or from small to large cross sectional areas, and the stages of the units are higher if the cross sectional areas of the units are larger; the resonant tubes are equal in length and unequal in cross sectional area; the cross sectional area of the resonant tube between the first and Nth stages of units is minimal, and the cross sectional areas of the other resonant tubes are enlarged along with the enlargement of the cross sectional areas of the units connected by the resonant tubes. When the system works, heat is converted into acoustic power under the temperature gradient of a reheater of each unit, the acoustic power is transmitted and amplified along the forward direction of the temperature gradient, and the amplified acoustic power is transmitted into the reheater of the unit of the next stage, and is amplified and transmitted to the unit of the stage after the next stage; most of the acoustic power which is amplified in multiple stages is consumed by the load, and the other is transmitted to the first stage of unit to continue the process. According to the system, an acoustic power index can be multiplied, so that a high-power load is favorably driven; the reheaters are positioned in a traveling-wave phase, so that thermoacoustic conversion efficiency is high.