The development of edge computing and Internet of Things technology has brought convenience to our lives, but the sensitive and private data collected are also more vulnerable to attack. Aiming at the data privacy security problem of edge-assisted Internet of Things, an outsourced mutual Private Set Intersection protocol is proposed. The protocol uses the ElGamal threshold encryption algorithm to rerandomize the encrypted elements to ensure all the set elements are calculated in the form of ciphertext. After that, the protocol maps the set elements to the corresponding hash bin under the execution of two hash functions and calculates the intersection in a bin-to-bin manner, reducing the number of comparisons of the set elements. In addition, the introduction of edge servers reduces the computational burden of participating users and achieves the fairness of the protocol. Finally, the IND-CPA security of the protocol is proved, and the performance of the protocol is compared with other relevant schemes. The evaluation results show that this protocol is superior to other related protocols in terms of lower computational overhead.