Over-threshold multi-party private set intersection (OT-MP-PSI) protocol is a variant of the conventional PSI, allowing m participants to jointly compute the set of threshold intersections for which at least t (t<=m) participants have the common element and ensuring that only the participant with the element knows whether it belongs to the threshold intersection and nothing else to the other elements. Existing solutions adapt those expensive public-key based cryptographic exponential operations which result in heavy computational overhead and low efficiency. In this paper, we design a novel cryptographic component, oblivious programmable pseudo-random function with secret sharing (OPPR-SS), which can achieve the oblivious pseudo-random secret sharing only rely on symmetric key based cryptographic operations. Furthermore, based on OPPR-SS, a double cloud assisted based OT-MP-PSI protocol is designed to deliver the task of sharing secrets and reconstructing secrets to the untrustworthy clouds, respectively, realizing that the participants with weak computational capability can complete the OT-MP-PSI protocol. Compared to the related work, our protocol has the best runtime and communication load among the existing OT-MP-PSI protocols. The number of communication rounds for the participants is constant and the communication complexity is O(n). The computational complexity of the sharing secrets cloud and reconstructing secrets cloud is only related to the number of symmetric-key based cryptographic operations.