Abstract: The existing feature retrieval private set intersection protocols have not imposed threshold constraints on the cardinality of the intersection that satisfy the predicate conditions, which makes it difficult to adapt to application scenarios that have threshold requirements on the size of data sets, such as carpool sharing and federated learning. To solve this problem, a two-party probabilistic predicate-constrained set size testing method that is secure against semi-honest adversaries is designed. This method can be used to judge whether the number of elements in the sender's input set that belong to the intersection and whose features meet the receiver's predicate conditions reaches the preset threshold. Moreover, based on this method, a two-party probabilistic threshold feature retrieval private set intersection protocol that is secure under the semi-honest model is proposed. During the execution of the protocol, only when the two-party probabilistic predicate-constrained set size test is passed, will the participants trigger the intersection computation that satisfies the predicate, and finally the receiver will obtain the intersection information that meets the predicate. Otherwise, the protocol will be terminated, and the receiver will not learn any information. Experimental results show that when the size of the participants' set is 2²⁰ and the threshold value is set to 2¹⁹, the total running time of the protocol is 11 seconds.