Private Set Intersection (PSI) protocols can securely compute the intersection of the private sets on the server and the client without revealing additional data. This work introduces the concept of Privacy-Preserving Feature Retrieved Private Set Intersection (<inline-formula> <tex-math notation="LaTeX">\mathsf {P^{2}FRPSI} </tex-math></inline-formula>). In <inline-formula> <tex-math notation="LaTeX">\mathsf {P^{2}FRPSI} </tex-math></inline-formula> protocols, the client can obtain the intersection that satisfies a given predicate without revealing the predicate and additional data. We formally define the <inline-formula> <tex-math notation="LaTeX">\mathsf {P^{2}FRPSI} </tex-math></inline-formula> protocol, including its inputs, outputs, functionality, and security. To achieve the privacy guarantee in <inline-formula> <tex-math notation="LaTeX">\mathsf {P^{2}FRPSI} </tex-math></inline-formula> protocols, a new two-party protocol is designed, namely Secure Secret Shared Retrieval (<inline-formula> <tex-math notation="LaTeX">\mathsf {S^{3}R} </tex-math></inline-formula>), which can be used to securely determine whether each item on the server satisfies the predicate. We construct an <inline-formula> <tex-math notation="LaTeX">\mathsf {S^{3}R} </tex-math></inline-formula> protocol and prove its security in the semi-honest model. On the basis of this, we design an efficient OT-based <inline-formula> <tex-math notation="LaTeX">\mathsf {P^{2}FRPSI} </tex-math></inline-formula> protocol and an easy-to-implement DH-based <inline-formula> <tex-math notation="LaTeX">\mathsf {P^{2}FRPSI} </tex-math></inline-formula> protocol and prove that they are secure in the semi-honest model. Our implementation shows that the OT-based <inline-formula> <tex-math notation="LaTeX">\mathsf {P^{2}FRPSI} </tex-math></inline-formula> protocol can perform the matching for about 1000K items in 3.8 seconds with a single thread. Moreover, the DH-based <inline-formula> <tex-math notation="LaTeX">\mathsf {P^{2}FRPSI} </tex-math></inline-formula> can perform the matching for about 7000K items in one hour with four threads, with communication totaling 1456 MB, while the OT-based <inline-formula> <tex-math notation="LaTeX">\mathsf {P^{2}FRPSI} </tex-math></inline-formula> protocol requires 1673 MB.