Private set computation is an important part of secure multi-party computation, which can perform certain set computations (such as intersection, union) among the legitimate participants without revealing their private information. However, the existing quantum private set computing protocols generally do not consider verification, so participants cannot determine whether the calculation results are correct or not. To solve this problem, a quantum private set computing protocol based on verification is proposed. In addition, this protocol can selectively solve private intersection or union problems. In performance analysis, the correctness and verifiability of the protocol are proved by examples, and the security of the protocol is also proved by external attack and participant attack.