Graph data structures’ ability of representing vertex relationships has made them increasingly popular in recent years. Amid this trend, many property graph datasets have been collected and made public to facilitate a variant of queries such as the aggregate queries that will be extensively exploited in this paper. While cloud deployment of both the datasets and query services is intriguing, it could raise privacy concerns related to user queries and results. In past years, many works on graph privacy have been put forth, however they either do not consider query privacy or cannot be adapted for aggregate queries. Some others consider queries over encrypted graphs but cannot protect access pattern privacy. In particular, when deploying them to handle queries over public graph datasets, the cloud server can infer additional information related to user queries. Aiming at this challenge, we propose a privacy-preserving property graph aggregate query scheme in this paper. Specifically, we first design new privacy-preserving vertex matching and matching update techniques, which securely initialize and update the mapping between vertices in the dataset and the user-specified patterns, respectively. Based on them, we construct our proposed scheme to achieve aggregate queries over public property graphs. Rigid security analysis shows that our proposed scheme can protect the privacy of user queries and results as well as achieve access pattern privacy. In addition, extensive experiments also demonstrate the efficiency of our scheme in terms of computational overheads.