Private Set Intersection （PSI） is an important solution for privacy information sharing. A fair multi-party PSI protocol based on cloud server was proposed for the unfairness caused by the existing protocols in which the parties involved do not have simultaneous access to the calculation results. Firstly， the storage of a sub-share of the private information in Garbled Bloom Filter （GBF） was accomplished by using hash mapping. Secondly， in order to avoid the leakage of the index value of each party’s set element during the interaction， combined with Oblivious Transfer （OT） technique， the share replacement of the stored information was realized. Finally， the bit-by-bit calculation was performed by the cloud server， and the results were returned to each party at the same time to ensure the fairness of each party’s access to the results. The correctness and security analysis of the protocol shows that the proposed protocol can achieve the fairness of the parties in obtaining the intersection results， and can resist the collusion of parties with the cloud server. The performance analysis shows that both of the computational complexity and the communication complexity of the proposed protocol are independent of the total number of elements contained in the set of participants. Under the same conditions， compared with Multi-party PSI protocol （MPSI）， practical multiparty maliciously-secure PSI protocol （PSImple） and Private Intersection Sum algorithm （PI-Sum）， the proposed protocol has less storage overhead， communication overhead and running time.