Considering agent's psychological behavior, a stable matching algorithm based on trilateral one-way non-cyclic preference order is proposed for the three-sided matching problem with one-way acyclic preference, Firstly, based on the one-way acyclic preference structure, the definition of three-sided matching with one-way acyclic preference and its stability are given, and the mathematical model based on the maximum cardinality and stable matching is established. Then, a search-optimization algorithm based on limited compromise is proposed, and the time complexity of the algorithm and the stability of the output scheme are calculated and proved respectively. Finally, an example is given to verify the feasibility and effectiveness of the proposed algorithm.