Aiming at three-sided matching problems with unidirectional acyclic preferences, a matching algorithm based on thresholds of preference order is proposed in this paper. First, based on the unidirectional acyclic structure, the definition of three-sided unidirectional acyclic matching and its stability are given, and the mathematical model to meet the stability requirements of the system is established. Second, thresholds of preference order are set to constrain the model, an edge-by-edge optimization algorithm in two stages with thresholds of preference order 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.