The present invention provides a multi-stage double-acting traveling-wave thermoacoustic system, comprising three elementary units, each elementary unit comprises a linear motor and a thermoacoustic conversion device; the linear motor comprises a piston and a cylinder, the piston can perform a straight reciprocating motion in the cylinder; each thermoacoustic conversion device comprises a main heat exchanger and a heat regenerator connected in sequence, and the heat regenerator is of a ladder structure; a set of a non-normal-temperature heat exchanger, a thermal buffer tube and an auxiliary heat exchanger is connected at each ladder of the heat regenerator; and the main heat exchanger and the auxiliary heat exchanger of each thermoacoustic conversion device are connected to cylinder cavities of different linear motors respectively forming a loop structure for flow of a gas medium. The multi-stage double-acting traveling-wave thermoacoustic system can improve the working performance of the multi-stage double-acting traveling-wave thermoacoustic system.